939:. Most classical results regarding subgroups of free groups acquired simple and straightforward proofs in this set-up and Stallings' method has become the standard tool in the theory for studying the subgroup structure of free groups, including both the algebraic and algorithmic questions (see ). In particular, Stallings subgroup graphs and Stallings foldings have been the used as a key tools in many attempts to approach the
1062:. The paper began with a humorous admission: "I have committed the sin of falsely proving Poincaré's Conjecture. But that was in another country; and besides, until now, no one has known about it." Despite its ironic title, Stallings' paper informed much of the subsequent research on exploring the algebraic aspects of the
268:
as well as an instructorship and a faculty appointment at
Princeton. Stallings joined the University of California at Berkeley as a faculty member in 1967 where he remained until his retirement in 1994. Even after his retirement, Stallings continued supervising UC Berkeley graduate students until
891:
proper since it connects a geometric property of a group (having more than one end) with its algebraic structure (admitting a splitting over a finite subgroup). Stallings' theorem spawned many subsequent alternative proofs by other mathematicians (e.g.) as well as many applications (e.g.). The
996:
and others. Stallings' work pointed out the importance of imposing some sort of "non-positive curvature" conditions on the complexes of groups in order for the theory to work well; such restrictions are not necessary in the one-dimensional case of Bass–Serre theory.
892:
theorem also motivated several generalizations and relative versions of
Stallings' result to other contexts, such as the study of the notion of relative ends of a group with respect to a subgroup, including a connection to
440:
and is a key example in the study of homological finiteness properties of groups. Robert Bieri later showed that the
Stallings group is exactly the kernel of the homomorphism from the direct product of three copies of the
883:) and then with the general case. Stalling's theorem yielded a positive solution to the long-standing open problem about characterizing finitely generated groups of cohomological dimension one as exactly the
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for describing subgroups of free groups, and also introduced a foldings technique (used for approximating and algorithmically obtaining the subgroup graphs) and the notion of what is now known as a
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Stallings proved this result in a series of works, first dealing with the torsion-free case (that is, a group with no nontrivial elements of finite
323:
297:
973:. The first paper in this direction was written by Stallings himself, with several subsequent generalizations of Stallings' folding methods in the
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1957:
896:. A comprehensive survey discussing, in particular, numerous applications and generalizations of Stallings' theorem, is given in a 2003 paper of
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from 1962 to 1965 and a Miller
Institute fellow from 1972 to 1973. Over the course of his career, Stallings had 22 doctoral students including
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After completing his PhD, Stallings held a number of postdoctoral and faculty positions, including being an NSF postdoctoral fellow at the
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2001:
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360:
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111:
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in 1956 (where he was one of the first two graduates in the university's Honors program) and he received a Ph.D. in
Mathematics from
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1967:
1847:
1607:
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Stallings was also interested in languages, and wrote one of the very few mathematical research papers in the constructed language
2038:
903:
Another influential paper of
Stallings is his 1983 article "Topology of finite graphs". Traditionally, the algebraic structure of
2382:
1754:
2831:
2581:
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1983:
1715:
1226:
2321:
2046:
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42:
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2258:
1906:
1592:
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Actes du Congrès
International des MathĂ©maticiens (Nice, 1970), Tome 2, pp. 165–167. Gauthier-Villars, Paris, 1971.
1344:
1047:
that engendered many alternative proofs, generalizations and applications (e.g. ), including a higher-dimensional analog.
316:
2178:
Dicks, Warren (1994). "Equivalence of the strengthened Hanna
Neumann conjecture and the amalgamated graph conjecture".
1713:
Stallings, John (1963). "A finitely presented group whose 3-dimensional integral homology is not finitely generated".
771:
2257:
Combinatorial and geometric group theory (New York, 2000/Hoboken, NJ, 2001), pp. 155–170, Contemp. Math., 296,
912:
119:
2698:
2306:
J. Almeida, and M. V. Volkov. "Subword complexity of profinite words and subgroups of free profinite semigroups."
2745:
326:
in
Berkeley in May 2000, was dedicated to the 65th birthday of Stallings. In 2002 a special issue of the journal
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Stallings, John R. (16 June 1993). "Sur un generalisation del notion de producto libere amalgamate de gruppos".
2394:
Ilya
Kapovich, Richard Weidmann, and Alexei Miasnikov. "Foldings, graphs of groups and the membership problem."
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2019:
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211:
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A James K. Whittemore Lecture in Mathematics given at Yale University, 1969. Yale Mathematical Monographs, 4.
1420:, Mathematical Sciences Research Institute Publications, vol. 19, New York: Springer, pp. 355–368,
1341:
Algebraic and geometric topology (Proc. Sympos. Pure Math., Stanford Univ., Stanford, Calif., 1976), Part 2
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1063:
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920:
888:
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219:
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where he had been a faculty member since 1967. He published over 50 papers, predominantly in the areas of
207:
96:
989:
980:
Stallings' 1991 paper "Non-positively curved triangles of groups" introduced and studied the notion of a
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651:
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1700:
1577:
1311:
1267:
1033:
947:
496:
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Springer–Verlag, New York, 2001. "Classics in Mathematics" series, reprint of the 1977 edition.
1224:(1963), "A finitely presented group whose 3-dimensional integral homology is not finitely generated",
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and R. J. Bean. Annals of Mathematics Studies, No. 60. Princeton University Press, Princeton, NJ 1966
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880:
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2338:(Berkeley, CA, 1988), pp. 355–368, Math. Sci. Res. Inst. Publ., 19, Springer, New York, 1991;
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916:
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328:
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2506:(Proc. The Univ. of Georgia Institute, 1961) pp. 95–100. Prentice-Hall, Englewood Cliffs, NJ
2164:
Proceedings of the Conference on Geometric and Combinatorial Group Theory, Part I (Haifa, 2000).
474:
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2224:
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1805:
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993:
548:. Bieri also showed that the Stallings group fits into a sequence of examples of groups of type
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Stallings' foldings method has been generalized and applied to other contexts, particularly in
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2681:
2487:
2452:
2429:
2339:
2262:
2127:
1963:
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1429:
1315:
1017:
433:
2550:
Louis Zulli. "Semibundle decompositions of 3-manifolds and the twisted cofundamental group."
741:
715:
578:
363:. (Stallings' proof was obtained independently from and shortly after the different proof of
2236:
2197:
1962:
Cambridge Studies in Advanced Mathematics, 17. Cambridge University Press, Cambridge, 1989.
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551:
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408:
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1953:
1933:
1870:
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1251:
1210:
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1021:
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and 100 doctoral descendants. He published over 50 papers, predominantly in the areas of
17:
1604:
1537:
2193:
2145:
Ilya Kapovich and Alexei Myasnikov. "Stallings foldings and subgroups of free groups."
1785:
1377:
1136:
2751:
2033:
1821:
1172:
Topology of 3-manifolds and related topics (Proc. The Univ. of Georgia Institute, 1961)
1044:
1029:
924:
631:(that is, with more than one "connected component at infinity"), which is now known as
628:
402:
370:
Using "engulfing" methods similar to those in his proof of the Poincaré conjecture for
1520:
2765:
2585:
2564:
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1809:
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Professor Emeritus John Stallings of the UC Berkeley Mathematics Department has died.
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is not equal to 4. This took on added significance when, as a consequence of work of
364:
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was dedicated to Stallings on the occasion of his 65th birthday. Stallings died from
203:
1401:
1104:
887:. Stallings' theorem about ends of groups is considered one of the first results in
642:
has more than one end if and only if this group admits a nontrivial splitting as an
2516:
2482:
Martin R. Bridson, and André Haefliger. "Metric spaces of non-positive curvature".
2117:
1055:
928:
893:
624:
609:
378:-dimensional space has a unique piecewise linear, hence also smooth, structure, if
226:. Stallings' most important contributions include a proof, in a 1960 paper, of the
2376:
2357:
and Mark Feighn. "Bounding the complexity of simplicial group actions on trees",
931:
framework. The paper introduced the notion of what is now commonly referred to as
2656:
V. N. Berestovskii. "Poincaré's conjecture and related statements." (in Russian)
1425:
2408:
2319:
Benjamin Steinberg. "A topological approach to inverse and regular semigroups."
1924:
Bulletin of the American Mathematical Society, vol. 74 (1968), pp. 361–364
1070:
322:
The conference "Geometric and Topological Aspects of Group Theory", held at the
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179:
147:
2255:
Positively generated subgroups of free groups and the Hanna Neumann conjecture.
1997:
2610:
1843:
1825:
1144:
1013:
1001:
923:. Stallings' paper put forward a topological approach based on the methods of
908:
884:
521:
the six elements coming from the choice of free bases for the three copies of
442:
353:
312:
290:
223:
129:
2451:(Trieste, 1990)", pp. 504–540, World Sci. Publ., River Edge, NJ, 1991.
2428:(Trieste, 1990), pp. 491–503, World Sci. Publ., River Edge, NJ, 1991;
2279:
Two-letter group codes that preserve aperiodicity of inverse finite automata.
1123:; Zeeman, E. C. (1962), "The piecewise-linear structure of Euclidean space",
214:. Stallings was a Professor Emeritus in the Department of Mathematics at the
1040:
951:
391:
258:
169:
1905:(Proc. Sympos. Pure Math., Vol. XVIII, New York, 1968) pp. 124–128.
2736:
2641:
2240:
2015:
1793:
1770:; Brady, Noel (1997), "Morse theory and finiteness properties of groups",
1605:
Geometric and Topological Aspects of Group Theory, conference announcement
2162:
Subgroups of free groups: a contribution to the Hanna Neumann conjecture.
985:
981:
904:
869:
658:
with finite edge stabilizers). More precisely, the theorem states that a
2535:
Alois Scharf. "Zur Faserung von Graphenmannigfaltigkeiten." (in German)
2589:
2565:"A random tunnel number one 3-manifold does not fiber over the circle."
2201:
2100:
1937:
1736:
1385:
1288:
1247:
1043:
over a circle. This is an important structural result in the theory of
2297:
Theoretical Computer Science, vol. 307 (2003), no. 1, pp. 77–92.
41:
2718:
1651:
2678:
GĂ©omĂ©trie au XXe siècle, 1930–2000 : histoire et horizons
1979:
1728:
1661:
Announcement at the website of the Department of Mathematics of the
1280:
1239:
616:
and Noel Brady and in the study of subgroups of direct products of
359:
An early significant result of Stallings is his 1960 proof of the
344:
Most of Stallings' mathematical contributions are in the areas of
2609:
John R. Stallings. Topology Seminar, Wisconsin, 1965. Edited by
1697:
Generalized Poincaré's conjecture in dimensions greater than four
608:. The Stallings group is a key object in the version of discrete
367:
who established the same result in dimensions bigger than four).
2664:(Izvestiya VUZ. Matematika), vol. 51 (2007), no. 9, 1–36
2424:
John R. Stallings. "Non-positively curved triangles of groups."
2081:(2003). "The geometry of abstract groups and their splittings".
301:
2628:
Mathematical Proceedings of the Cambridge Philosophical Society
2227:(2001). "The rank three case of the Hanna Neumann conjecture".
2061:"Ends of group pairs and non-positively curved cube complexes."
1538:"John R. Stallings Jr., 73, California Mathematician, Is Dead"
627:
is an algebraic characterization of groups with more than one
436:
with a finite 3-skeleton. This example came to be called the
2624:"Splitting homomorphisms and the geometrization conjecture."
1265:(1968), "On torsion-free groups with infinitely many ends",
2502:
John R. Stallings. "On fibering certain 3-manifolds." 1962
1844:"Subgroups of direct products of elementarily free groups."
654:, if and only if the group admits a nontrivial action on a
2680:. Montréal, Presses internationales Polytechnique, 2005.
1749:
Robert Bieri. "Homological dimension of discrete groups."
1511:
press release, January 12, 2009. Accessed January 26, 2009
1901:
John Stallings. "Groups of cohomological dimension one."
1455:
Group theory from a geometrical viewpoint (Trieste, 1990)
2660:
vol. 51 (2000), no. 9, pp. 3–41; translation in
984:. This notion was the starting point for the theory of
1457:, River Edge, NJ: World Scientific, pp. 491–903,
397:
In a 1963 paper Stallings constructed an example of a
1826:"The subgroups of direct products of surface groups".
1453:(1991), "Non-positively curved triangles of groups",
1343:, Proc. Sympos. Pure Math., XXXII, Providence, R.I.:
842:
774:
744:
718:
675:
581:
554:
527:
499:
477:
450:
411:
1824:, James Howie, Charles F. Miller, and Hamish Short.
1703:(2nd Ser.), vol. 74 (1961), no. 2, pp. 391–406
2699:"Mathematician John Stallings died last year at 73"
2658:
Izvestiya Vysshikh Uchebnykh Zavedenii. Matematika.
2381:, The Epstein birthday schrift, pp. 139–158,
2005:, vol. 11 (1977/78), no. 1–3, pp. 75–82
1339:(1978), "Constructions of fibred knots and links",
175:
163:
153:
143:
125:
106:
92:
73:
51:
32:
2295:Image reducing words and subgroups of free groups.
1506:Mathematician John Stallings died last year at 73.
1234:(4), The Johns Hopkins University Press: 541–543,
1125:Proceedings of the Cambridge Philosophical Society
860:
828:
756:
730:
700:
669:admits a splitting as an amalgamated free product
600:
567:
540:
513:
485:
463:
424:
361:Poincaré conjecture in dimensions greater than six
228:Poincaré Conjecture in dimensions greater than six
112:Poincaré Conjecture in dimensions greater than six
2758:, vol. 56 (2009), no. 11, pp. 1410 1417
2396:International Journal of Algebra and Computation
1887:On torsion-free groups with infinitely many ends.
1863:Subgroups of direct products of two limit groups.
1193:(1965), "Homology and central series of groups",
401:with infinitely generated 3-dimensional integral
374:> 6, Stallings proved that ordinary Euclidean
2308:International Journal of Algebra and Computation
2068:(3), vol. 71 (1995), no. 3, pp. 585–617
1980:"A new proof of the annulus and torus theorems."
946:Stallings subgroup graphs can also be viewed as
829:{\displaystyle G=\langle H,t|t^{-1}Kt=L\rangle }
356:) and on the interplay between these two areas.
1757:, Department of Pure Mathematics, London, 1976.
2802:Institute for Advanced Study visiting scholars
2470:Proceedings of the London Mathematical Society
2411:, "Membership problem for the modular group",
2065:Proceedings of the London Mathematical Society
296:Stallings delivered an invited address as the
2484:Grundlehren der Mathematischen Wissenschaften
2293:D. S. Ananichev, A. Cherubini, M. V. Volkov.
2277:Jean-Camille Birget, and Stuart W. Margolis.
1998:"Relative version of a theorem of Stallings."
1681:Bulletin of the American Mathematical Society
1574:Group theory and three-dimensional manifolds.
1092:Bulletin of the American Mathematical Society
304:in 1970 and a James K. Whittemore Lecture at
242:John Stallings was born on July 22, 1935, in
8:
2756:Notices of the American Mathematical Society
2363:, vol. 103, (1991), no. 3, pp. 449–469
2108:, vol. 71 (1983), no. 3, pp. 551–565
2023:, vol. 140 (2000), no. 3, pp. 605–637
1987:, vol. 102 (1980), no. 2, pp. 241–277
1851:, vol. 17 (2007), no. 2, pp. 385–403
1308:Group theory and three-dimensional manifolds
823:
781:
665:has more than one end if and only if either
2676:. "Autour de l'hypothèse de Poincaré". in:
2631:, vol. 129 (2000), no. 2, pp. 291–300
2563:Nathan M. Dunfield, and Dylan P. Thurston.
2415:, vol. 37 (2007), no. 2, pp. 425–459.
2325:, vol. 208 (2003), no. 2, pp. 367–396
2310:, vol. 16 (2006), no. 2, pp. 221–258.
2050:, vol. 196 (2000), no. 2, pp. 461–506
1170:(1962), "On fibering certain 3-manifolds",
969:and studying the subgroup structure of the
2817:University of California, Berkeley faculty
2554:, vol. 79 (1997), no. 2, pp. 159–172
2504:Topology of 3-manifolds and related topics
2447:. "Complexes of groups and orbihedra" in:
2398:, vol. 15 (2005), no. 1, pp. 95–128.
2334:John R. Stallings. "Foldings of G-trees."
2284:, vol. 76 (2008), no. 1, pp. 159–168
1418:Arboreal group theory (Berkeley, CA, 1988)
1052:"How not to prove the Poincaré conjecture"
650:over a finite group (that is, in terms of
202:(July 22, 1935 – November 24, 2008) was a
40:
29:
2717:
2642:"On the Grigorchuk–Kurchanov conjecture."
2605:
2603:
2449:Group theory from a geometrical viewpoint
2426:Group theory from a geometrical viewpoint
2151:, vol. 248 (2002), no. 2, 608–668
1103:
950:and they have also found applications in
915:using combinatorial methods, such as the
841:
802:
793:
773:
743:
717:
689:
674:
586:
580:
559:
553:
532:
526:
507:
506:
498:
479:
478:
476:
455:
449:
416:
410:
2473:(3) 65 (1992), no. 1, pp. 199–224.
2385:, 1, Geom. Topol. Publ., Coventry, 1998.
324:Mathematical Sciences Research Institute
298:International Congress of Mathematicians
2521:3-manifolds which fiber over a surface.
1921:Groups of dimension 1 are locally free.
1892:(2), vol. 88 (1968), pp. 312–334.
1876:, vol. 14 (2007), no. 4, 547–558.
1635:MacTutor History of Mathematics Archive
1501:
1499:
1497:
1495:
1493:
1491:
1489:
1485:
768:admits a splitting as an HNN extension
633:Stallings' theorem about ends of groups
390:in 1982, it was shown that 4-space has
206:known for his seminal contributions to
2572:, vol. 10 (2006), pp. 2431–2499
2486:, 319. Springer-Verlag, Berlin, 1999.
2141:
2139:
2014:Martin J. Dunwoody and E. L. Swenson.
1580:, New Haven, Conn.–London, 1971.
971:fundamental groups of graphs of groups
232:Stallings theorem about ends of groups
116:Stallings theorem about ends of groups
2032:G. Peter Scott, and Gadde A. Swarup.
1751:Queen Mary College Mathematical Notes
1568:
1566:
1531:
1529:
1362:(1983), "Topology of finite graphs",
1275:(2), Annals of Mathematics: 312–334,
230:and a proof, in a 1971 paper, of the
7:
2797:21st-century American mathematicians
2792:20th-century American mathematicians
2647:107 (2002), no. 4, pp. 451–461
1860:Martin R. Bridson, and James Howie.
1842:Martin R. Bridson, and James Howie.
1833:, vol. 92 (2002), pp. 95–103.
1683:, vol. 66 (1960), pp. 485–488.
1663:University of California at Berkeley
216:University of California at Berkeley
158:University of California at Berkeley
2597:, vol. 40 (1966), pp. 153–160
2590:2Fibering manifolds over a circle."
2541:, vol. 215 (1975), pp. 35–45.
2526:, vol. 94 (1972), pp. 189–205
2467:Jon Corson. "Complexes of groups."
2002:Journal of Pure and Applied Algebra
1903:Applications of Categorical Algebra
1590:Frank Nelson Cole Prize in Algebra.
1536:Chang, Kenneth (January 18, 2009),
965:for approximating group actions on
612:for cubical complexes developed by
2168:, vol. 94 (2002), pp. 33–43.
1000:Among Stallings' contributions to
623:Stallings' most famous theorem in
313:Frank Nelson Cole Prize in Algebra
249:Stallings received his B.Sc. from
130:Frank Nelson Cole Prize in Algebra
25:
2594:Commentarii Mathematici Helvetici
1943:2 (1982), no. 1, pp. 15–23.
1848:Geometric and Functional Analysis
1523:Volume 3, Issue 4; November 2002.
977:context by other mathematicians.
514:{\displaystyle 1\in \mathbb {Z} }
394:, in fact uncountably many such.
2383:Geometry and Topology Monographs
1405:, with over 100 recent citations
988:(a higher-dimensional analog of
2822:People from Morrilton, Arkansas
2640:Tullio Ceccherini-Silberstein.
2524:American Journal of Mathematics
1984:American Journal of Mathematics
1716:American Journal of Mathematics
1227:American Journal of Mathematics
1105:10.1090/s0002-9904-1960-10511-3
405:and, moreover, not of the type
271:Alfred P. Sloan Research fellow
257:in 1959 under the direction of
2322:Pacific Journal of Mathematics
2083:Revista Matemática Complutense
2047:Pacific Journal of Mathematics
2016:"The algebraic torus theorem."
794:
352:(particularly the topology of
1:
2807:University of Arkansas alumni
2741:Mathematics Genealogy Project
2552:Topology and its Applications
2259:American Mathematical Society
2035:An algebraic annulus theorem.
1907:American Mathematical Society
1874:Mathematical Research Letters
1593:American Mathematical Society
1558:Group theory and 3-manifolds.
1345:American Mathematical Society
1088:"Polyhedral homotopy spheres"
1024:, such that this subgroup is
1008:. The theorem states that if
1004:, the most well-known is the
701:{\displaystyle G=A\ast _{C}B}
317:American Mathematical Society
120:Stallings graphs and automata
2827:Mathematicians from Arkansas
2101:"Topology of finite graphs."
1677:Polyhedral homotopy spheres.
1547:. Accessed January 26, 2009.
1426:10.1007/978-1-4612-3142-4_14
1207:10.1016/0021-8693(65)90017-7
1058:reformulation of the famous
486:{\displaystyle \mathbb {Z} }
2812:Princeton University alumni
2123:Combinatorial Group Theory.
1665:. Accessed December 4, 2008
1006:Stallings fibration theorem
432:, that is, not admitting a
2848:
2752:Remembering John Stallings
1050:A 1965 paper of Stallings
913:combinatorial group theory
635:. Stallings proved that a
493:of integers that sends to
340:Mathematical contributions
18:John Robert Stallings, Jr.
2413:SIAM Journal on Computing
1145:10.1017/S0305004100036756
1012:is a compact irreducible
917:Schreier rewriting method
861:{\displaystyle K,L\leq H}
200:John Robert Stallings Jr.
193:
136:
39:
2360:Inventiones Mathematicae
2261:, Providence, RI, 2002;
2181:Inventiones Mathematicae
2160:J. Meakin, and P. Weil.
2105:Inventiones Mathematicae
2020:Inventiones Mathematicae
1959:Groups acting on graphs.
1909:, Providence, R.I, 1970.
1773:Inventiones Mathematicae
1640:University of St Andrews
1365:Inventiones Mathematicae
941:Hanna Neumann conjecture
933:Stallings subgroup graph
927:that also used a simple
894:CAT(0) cubical complexes
660:finitely generated group
644:amalgamated free product
637:finitely generated group
399:finitely presented group
392:exotic smooth structures
350:low-dimensional topology
2645:Manuscripta Mathematica
2569:Geometry & Topology
2229:Journal of Group Theory
1614:, atlas-conferences.com
921:Nielsen transformations
757:{\displaystyle C\neq B}
731:{\displaystyle C\neq A}
601:{\displaystyle F_{n+1}}
311:Stallings received the
269:2005. Stallings was an
46:2006 photo of Stallings
2832:Sloan Research Fellows
889:geometric group theory
862:
830:
758:
732:
702:
602:
569:
542:
515:
487:
471:to the additive group
465:
426:
346:geometric group theory
336:on November 24, 2008.
287:geometric group theory
251:University of Arkansas
220:geometric group theory
208:geometric group theory
97:University of Arkansas
27:American mathematician
2538:Mathematische Annalen
2336:Arboreal group theory
2241:10.1515/jgth.2001.012
1890:Annals of Mathematics
1794:10.1007/s002220050168
1701:Annals of Mathematics
1578:Yale University Press
1312:Yale University Press
1268:Annals of Mathematics
1066:(see, for example,).
948:finite-state automata
925:covering space theory
863:
831:
759:
733:
703:
603:
570:
568:{\displaystyle F_{n}}
543:
541:{\displaystyle F_{2}}
516:
488:
466:
464:{\displaystyle F_{2}}
427:
425:{\displaystyle F_{3}}
2787:American topologists
2120:and Paul E. Schupp.
1938:"Cutting up graphs."
1626:Robertson, Edmund F.
1521:All things academic.
1032:by this subgroup is
911:has been studied in
840:
772:
742:
716:
673:
579:
552:
525:
497:
475:
448:
409:
289:and the topology of
266:University of Oxford
255:Princeton University
222:and the topology of
101:Princeton University
85:Berkeley, California
2662:Russian Mathematics
2407:Yuri Gurevich, and
2225:Formanek, Edward W.
2194:1994InMat.117..373D
2166:Geometriae Dedicata
2099:John R. Stallings.
1918:John R. Stallings.
1885:John R. Stallings.
1830:Geometriae Dedicata
1786:1997InMat.129..445B
1624:O'Connor, John J.;
1556:John R. Stallings.
1378:1983InMat..71..551S
1178:, pp. 95–100,
1137:1962PCPS...58..481S
1064:Poincaré conjecture
1060:Poincaré conjecture
1002:3-manifold topology
986:complexes of groups
329:Geometriae Dedicata
244:Morrilton, Arkansas
212:3-manifold topology
66:Morrilton, Arkansas
2748:of John Stallings.
2701:. 12 January 2009.
2202:10.1007/BF01232249
2148:Journal of Algebra
2041:2007-07-15 at the
1954:Martin J. Dunwoody
1934:Martin J. Dunwoody
1869:2008-07-05 at the
1755:Queen Mary College
1657:2008-12-28 at the
1610:2008-09-06 at the
1543:The New York Times
1451:Stallings, John R.
1410:Stallings, John R.
1386:10.1007/BF02095993
1360:Stallings, John R.
1347:, pp. 55–60,
1337:Stallings, John R.
1304:Stallings, John R.
1263:Stallings, John R.
1195:Journal of Algebra
1191:Stallings, John R.
1168:Stallings, John R.
1121:Stallings, John R.
1084:Stallings, John R.
1028:and such that the
1026:finitely generated
982:triangle of groups
858:
826:
754:
728:
708:, where the group
698:
598:
565:
538:
511:
483:
461:
422:
283:J. Hyam Rubinstein
279:Stephen M. Gersten
188:J. Hyam Rubinstein
184:Stephen M. Gersten
2737:John R. Stallings
2378:Folding sequences
2132:978-3-540-41158-1
1996:Gadde A. Swarup.
1952:Warren Dicks and
1822:Martin R. Bridson
1464:978-981-02-0442-6
1435:978-0-387-97518-4
1412:(1991), "Folding
1321:978-0-300-01397-9
1271:, Second Series,
1018:fundamental group
990:Bass–Serre theory
975:Bass–Serre theory
963:Bass–Serre theory
937:Stallings folding
652:Bass–Serre theory
434:classifying space
197:
196:
176:Doctoral students
138:Scientific career
77:November 24, 2008
34:John R. Stallings
16:(Redirected from
2839:
2724:
2723:
2721:
2709:
2703:
2702:
2695:
2689:
2688:, 9782553013997.
2674:Valentin Poénaru
2671:
2665:
2654:
2648:
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2614:
2607:
2598:
2579:
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2533:
2527:
2515:John Hempel and
2513:
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2494:
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2012:
2006:
1994:
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1768:Bestvina, Mladen
1764:
1758:
1747:
1741:
1740:
1710:
1704:
1690:
1684:
1674:John Stallings.
1672:
1666:
1649:
1643:
1642:
1630:"John Stallings"
1621:
1615:
1602:
1596:
1587:
1581:
1572:John Stallings.
1570:
1561:
1554:
1548:
1546:
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1524:
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1512:
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1475:
1446:
1404:
1355:
1332:
1299:
1258:
1217:
1186:
1163:
1116:
1107:
992:), developed by
956:computer science
867:
865:
864:
859:
835:
833:
832:
827:
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809:
797:
763:
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735:
734:
729:
707:
705:
704:
699:
694:
693:
607:
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599:
597:
596:
575:but not of type
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384:Michael Freedman
165:Doctoral advisor
80:
61:
59:
44:
30:
21:
2847:
2846:
2842:
2841:
2840:
2838:
2837:
2836:
2782:Group theorists
2762:
2761:
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2728:
2727:
2711:
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2582:William Browder
2580:
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2462:
2445:André Haefliger
2443:
2439:
2423:
2419:
2406:
2402:
2393:
2389:
2373:Martin Dunwoody
2371:
2367:
2355:Mladen Bestvina
2353:
2349:
2333:
2329:
2318:
2314:
2305:
2301:
2292:
2288:
2282:Semigroup Forum
2276:
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2252:
2248:
2223:Dicks, Warren;
2222:
2221:
2217:
2177:
2176:
2172:
2159:
2155:
2144:
2137:
2118:Roger C. Lyndon
2116:
2112:
2098:
2094:
2077:
2076:
2072:
2059:Michah Sageev.
2058:
2054:
2043:Wayback Machine
2031:
2027:
2013:
2009:
1995:
1991:
1977:
1973:
1951:
1947:
1932:
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1871:Wayback Machine
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1729:10.2307/2373106
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1659:Wayback Machine
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1302:
1281:10.2307/1970577
1261:
1240:10.2307/2373106
1222:Stallings, John
1220:
1189:
1166:
1119:
1082:
1079:
1056:group-theoretic
1045:Haken manifolds
1034:infinite cyclic
1022:normal subgroup
994:André Haefliger
929:graph-theoretic
838:
837:
798:
770:
769:
740:
739:
714:
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685:
671:
670:
614:Mladen Bestvina
582:
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451:
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438:Stallings group
412:
407:
406:
388:Simon Donaldson
342:
334:prostate cancer
306:Yale University
240:
186:
182:
99:
93:Alma mater
88:
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35:
28:
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15:
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5:
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2789:
2784:
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2749:
2743:
2732:
2731:External links
2729:
2726:
2725:
2704:
2690:
2666:
2649:
2633:
2622:Robert Myers.
2615:
2599:
2574:
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2508:
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2400:
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2327:
2312:
2299:
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2270:
2246:
2235:(2): 113–151.
2215:
2188:(3): 373–389.
2170:
2153:
2135:
2110:
2092:
2079:Wall, C. T. C.
2070:
2052:
2025:
2007:
1989:
1971:
1945:
1926:
1911:
1894:
1878:
1853:
1835:
1814:
1780:(3): 445–470,
1759:
1742:
1723:(4): 541–543.
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1372:(3): 551–565,
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1218:
1201:(2): 170–181,
1187:
1164:
1131:(3): 481–488,
1117:
1098:(6): 485–488,
1078:
1077:Selected works
1075:
1030:quotient group
954:theory and in
857:
854:
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712:is finite and
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107:Known for
104:
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81:(aged 73)
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2586:Jerome Levine
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2492:3-540-64324-9
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2457:981-02-0442-6
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2185:
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2161:
2156:
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2018:
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1992:
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1974:
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625:group theory
622:
618:limit groups
610:Morse theory
437:
396:
379:
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369:
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327:
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199:
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154:Institutions
137:
79:(2008-11-24)
2777:2008 deaths
2772:1935 births
2409:Paul Schupp
2089:(1): 5–101.
1509:UC Berkeley
1071:Interlingua
1020:contains a
909:free groups
885:free groups
868:are finite
354:3-manifolds
291:3-manifolds
275:Marc Culler
224:3-manifolds
180:Marc Culler
148:Mathematics
2766:Categories
2611:R. H. Bing
1014:3-manifold
443:free group
58:1935-07-22
2746:home page
2210:121902432
1810:120422255
1416:-trees",
1161:120418488
952:semigroup
905:subgroups
870:subgroups
853:≤
824:⟩
804:−
782:⟨
749:≠
723:≠
687:∗
646:or as an
504:∈
319:in 1970.
315:from the
308:in 1969.
259:Ralph Fox
238:Biography
170:Ralph Fox
110:proof of
2039:Archived
1867:Archived
1655:Archived
1608:Archived
1402:16643207
1306:(1971),
1086:(1960),
2739:at the
2190:Bibcode
1802:1465330
1782:Bibcode
1737:2373106
1473:1170374
1444:1105341
1394:0695906
1374:Bibcode
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1330:0415622
1297:0228573
1289:1970577
1256:0158917
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281:, and
144:Fields
132:(1971)
126:Awards
87:, U.S.
68:, U.S.
2714:arXiv
2206:S2CID
1806:S2CID
1733:JSTOR
1480:Notes
1398:S2CID
1285:JSTOR
1244:JSTOR
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967:trees
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764:, or
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