928:. 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
1051:. 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
257:
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
880:
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
985:
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.
881:
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
429:
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
872:) 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
312:
286:
962:. 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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1946:
885:. 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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1990:
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100:
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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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1956:
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Stallings was also interested in languages, and wrote one of the very few mathematical research papers in the constructed language
2027:
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Another influential paper of
Stallings is his 1983 article "Topology of finite graphs". Traditionally, the algebraic structure of
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1743:
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1972:
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2310:
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632:
31:
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1895:
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Actes du Congrès
International des MathĂ©maticiens (Nice, 1970), Tome 2, pp. 165–167. Gauthier-Villars, Paris, 1971.
1333:
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that engendered many alternative proofs, generalizations and applications (e.g. ), including a higher-dimensional analog.
305:
2167:
Dicks, Warren (1994). "Equivalence of the strengthened Hanna
Neumann conjecture and the amalgamated graph conjecture".
1702:
Stallings, John (1963). "A finitely presented group whose 3-dimensional integral homology is not finitely generated".
760:
2246:
Combinatorial and geometric group theory (New York, 2000/Hoboken, NJ, 2001), pp. 155–170, Contemp. Math., 296,
901:
108:
2687:
2295:
J. Almeida, and M. V. Volkov. "Subword complexity of profinite words and subgroups of free profinite semigroups."
2734:
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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".
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Ilya
Kapovich, Richard Weidmann, and Alexei Miasnikov. "Foldings, graphs of groups and the membership problem."
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2008:
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200:
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A James K. Whittemore Lecture in Mathematics given at Yale University, 1969. Yale Mathematical Monographs, 4.
1409:, Mathematical Sciences Research Institute Publications, vol. 19, New York: Springer, pp. 355–368,
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Algebraic and geometric topology (Proc. Sympos. Pure Math., Stanford Univ., Stanford, Calif., 1976), Part 2
2557:
1052:
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877:
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208:
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where he had been a faculty member since 1967. He published over 50 papers, predominantly in the areas of
196:
85:
978:
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Stallings' 1991 paper "Non-positively curved triangles of groups" introduced and studied the notion of a
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1300:
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1022:
936:
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Springer–Verlag, New York, 2001. "Classics in Mathematics" series, reprint of the 1977 edition.
1213:(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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2327:(Berkeley, CA, 1988), pp. 355–368, Math. Sci. Res. Inst. Publ., 19, Springer, New York, 1991;
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2154:
1818:
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905:
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317:
232:
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2495:(Proc. The Univ. of Georgia Institute, 1961) pp. 95–100. Prentice-Hall, Englewood Cliffs, NJ
2153:
Proceedings of the Conference on Geometric and Combinatorial Group Theory, Part I (Haifa, 2000).
463:
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537:. 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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2441:
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1952:
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1418:
1304:
1006:
422:
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Louis Zulli. "Semibundle decompositions of 3-manifolds and the twisted cofundamental group."
730:
704:
567:
352:. (Stallings' proof was obtained independently from and shortly after the different proof of
2225:
2186:
1951:
Cambridge Studies in Advanced Mathematics, 17. Cambridge University Press, Cambridge, 1989.
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and 100 doctoral descendants. He published over 50 papers, predominantly in the areas of
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1526:
2182:
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Ilya Kapovich and Alexei Myasnikov. "Stallings foldings and subgroups of free groups."
1774:
1366:
1125:
2740:
2022:
1810:
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Topology of 3-manifolds and related topics (Proc. The Univ. of Georgia Institute, 1961)
1033:
1018:
913:
620:(that is, with more than one "connected component at infinity"), which is now known as
617:
391:
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Using "engulfing" methods similar to those in his proof of the Poincaré conjecture for
1509:
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2574:
2553:
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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
353:
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was dedicated to Stallings on the occasion of his 65th birthday. Stallings died from
192:
1390:
1093:
876:. Stallings' theorem about ends of groups is considered one of the first results in
631:
has more than one end if and only if this group admits a nontrivial splitting as an
2505:
2471:
Martin R. Bridson, and André Haefliger. "Metric spaces of non-positive curvature".
2106:
1044:
917:
882:
613:
598:
367:-dimensional space has a unique piecewise linear, hence also smooth, structure, if
215:. Stallings' most important contributions include a proof, in a 1960 paper, of the
2365:
2346:
and Mark Feighn. "Bounding the complexity of simplicial group actions on trees",
920:
framework. The paper introduced the notion of what is now commonly referred to as
2645:
V. N. Berestovskii. "Poincaré's conjecture and related statements." (in Russian)
1414:
2397:
2308:
Benjamin Steinberg. "A topological approach to inverse and regular semigroups."
1913:
Bulletin of the American Mathematical Society, vol. 74 (1968), pp. 361–364
1059:
311:
The conference "Geometric and Topological Aspects of Group Theory", held at the
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168:
136:
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Positively generated subgroups of free groups and the Hanna Neumann conjecture.
1986:
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1832:
1814:
1133:
1002:
990:
912:. Stallings' paper put forward a topological approach based on the methods of
897:
873:
510:
the six elements coming from the choice of free bases for the three copies of
431:
342:
301:
279:
212:
118:
2440:(Trieste, 1990)", pp. 504–540, World Sci. Publ., River Edge, NJ, 1991.
2417:(Trieste, 1990), pp. 491–503, World Sci. Publ., River Edge, NJ, 1991;
2268:
Two-letter group codes that preserve aperiodicity of inverse finite automata.
1112:; Zeeman, E. C. (1962), "The piecewise-linear structure of Euclidean space",
203:. Stallings was a Professor Emeritus in the Department of Mathematics at the
1029:
940:
380:
247:
158:
1894:(Proc. Sympos. Pure Math., Vol. XVIII, New York, 1968) pp. 124–128.
2725:
2630:
2229:
2004:
1782:
1759:; Brady, Noel (1997), "Morse theory and finiteness properties of groups",
1594:
Geometric and Topological Aspects of Group Theory, conference announcement
2151:
Subgroups of free groups: a contribution to the Hanna Neumann conjecture.
974:
970:
893:
858:
647:
with finite edge stabilizers). More precisely, the theorem states that a
2524:
Alois Scharf. "Zur Faserung von Graphenmannigfaltigkeiten." (in German)
2578:
2554:"A random tunnel number one 3-manifold does not fiber over the circle."
2190:
2089:
1926:
1725:
1374:
1277:
1236:
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over a circle. This is an important structural result in the theory of
2286:
Theoretical Computer Science, vol. 307 (2003), no. 1, pp. 77–92.
30:
2707:
1640:
2667:
GĂ©omĂ©trie au XXe siècle, 1930–2000 : histoire et horizons
1968:
1717:
1650:
Announcement at the website of the Department of Mathematics of the
1269:
1228:
605:
and Noel Brady and in the study of subgroups of direct products of
348:
An early significant result of Stallings is his 1960 proof of the
333:
Most of Stallings' mathematical contributions are in the areas of
2598:
John R. Stallings. Topology Seminar, Wisconsin, 1965. Edited by
1686:
Generalized Poincaré's conjecture in dimensions greater than four
597:. The Stallings group is a key object in the version of discrete
356:
who established the same result in dimensions bigger than four).
2653:(Izvestiya VUZ. Matematika), vol. 51 (2007), no. 9, 1–36
2413:
John R. Stallings. "Non-positively curved triangles of groups."
2070:(2003). "The geometry of abstract groups and their splittings".
290:
2617:
Mathematical Proceedings of the Cambridge Philosophical Society
2216:(2001). "The rank three case of the Hanna Neumann conjecture".
2050:"Ends of group pairs and non-positively curved cube complexes."
1527:"John R. Stallings Jr., 73, California Mathematician, Is Dead"
616:
is an algebraic characterization of groups with more than one
425:
with a finite 3-skeleton. This example came to be called the
2613:"Splitting homomorphisms and the geometrization conjecture."
1254:(1968), "On torsion-free groups with infinitely many ends",
2491:
John R. Stallings. "On fibering certain 3-manifolds." 1962
1833:"Subgroups of direct products of elementarily free groups."
643:, if and only if the group admits a nontrivial action on a
2669:. Montréal, Presses internationales Polytechnique, 2005.
1738:
Robert Bieri. "Homological dimension of discrete groups."
1500:
press release, January 12, 2009. Accessed January 26, 2009
1890:
John Stallings. "Groups of cohomological dimension one."
1444:
Group theory from a geometrical viewpoint (Trieste, 1990)
2649:
vol. 51 (2000), no. 9, pp. 3–41; translation in
973:. This notion was the starting point for the theory of
1446:, River Edge, NJ: World Scientific, pp. 491–903,
386:
In a 1963 paper Stallings constructed an example of a
1815:"The subgroups of direct products of surface groups".
1442:(1991), "Non-positively curved triangles of groups",
1332:, Proc. Sympos. Pure Math., XXXII, Providence, R.I.:
831:
763:
733:
707:
664:
570:
543:
516:
488:
466:
439:
400:
1813:, James Howie, Charles F. Miller, and Hamish Short.
1692:(2nd Ser.), vol. 74 (1961), no. 2, pp. 391–406
2688:"Mathematician John Stallings died last year at 73"
2647:
Izvestiya Vysshikh Uchebnykh Zavedenii. Matematika.
2370:, The Epstein birthday schrift, pp. 139–158,
1994:, vol. 11 (1977/78), no. 1–3, pp. 75–82
1328:(1978), "Constructions of fibred knots and links",
164:
152:
142:
132:
114:
95:
81:
62:
40:
21:
2284:Image reducing words and subgroups of free groups.
1495:Mathematician John Stallings died last year at 73.
1223:(4), The Johns Hopkins University Press: 541–543,
1114:Proceedings of the Cambridge Philosophical Society
849:
817:
745:
719:
689:
658:admits a splitting as an amalgamated free product
589:
556:
529:
502:
474:
452:
413:
350:Poincaré conjecture in dimensions greater than six
217:Poincaré Conjecture in dimensions greater than six
101:Poincaré Conjecture in dimensions greater than six
2747:, vol. 56 (2009), no. 11, pp. 1410 1417
2385:International Journal of Algebra and Computation
1876:On torsion-free groups with infinitely many ends.
1852:Subgroups of direct products of two limit groups.
1182:(1965), "Homology and central series of groups",
390:with infinitely generated 3-dimensional integral
363:> 6, Stallings proved that ordinary Euclidean
2297:International Journal of Algebra and Computation
2057:(3), vol. 71 (1995), no. 3, pp. 585–617
1969:"A new proof of the annulus and torus theorems."
935:Stallings subgroup graphs can also be viewed as
818:{\displaystyle G=\langle H,t|t^{-1}Kt=L\rangle }
345:) and on the interplay between these two areas.
1746:, Department of Pure Mathematics, London, 1976.
2791:Institute for Advanced Study visiting scholars
2459:Proceedings of the London Mathematical Society
2400:, "Membership problem for the modular group",
2054:Proceedings of the London Mathematical Society
285:Stallings delivered an invited address as the
2473:Grundlehren der Mathematischen Wissenschaften
2282:D. S. Ananichev, A. Cherubini, M. V. Volkov.
2266:Jean-Camille Birget, and Stuart W. Margolis.
1987:"Relative version of a theorem of Stallings."
1670:Bulletin of the American Mathematical Society
1563:Group theory and three-dimensional manifolds.
1081:Bulletin of the American Mathematical Society
293:in 1970 and a James K. Whittemore Lecture at
231:John Stallings was born on July 22, 1935, in
8:
2745:Notices of the American Mathematical Society
2352:, vol. 103, (1991), no. 3, pp. 449–469
2097:, vol. 71 (1983), no. 3, pp. 551–565
2012:, vol. 140 (2000), no. 3, pp. 605–637
1976:, vol. 102 (1980), no. 2, pp. 241–277
1840:, vol. 17 (2007), no. 2, pp. 385–403
1297:Group theory and three-dimensional manifolds
812:
770:
654:has more than one end if and only if either
2665:. "Autour de l'hypothèse de Poincaré". in:
2620:, vol. 129 (2000), no. 2, pp. 291–300
2552:Nathan M. Dunfield, and Dylan P. Thurston.
2404:, vol. 37 (2007), no. 2, pp. 425–459.
2314:, vol. 208 (2003), no. 2, pp. 367–396
2299:, vol. 16 (2006), no. 2, pp. 221–258.
2039:, vol. 196 (2000), no. 2, pp. 461–506
1159:(1962), "On fibering certain 3-manifolds",
958:and studying the subgroup structure of the
2806:University of California, Berkeley faculty
2543:, vol. 79 (1997), no. 2, pp. 159–172
2493:Topology of 3-manifolds and related topics
2436:. "Complexes of groups and orbihedra" in:
2387:, vol. 15 (2005), no. 1, pp. 95–128.
2323:John R. Stallings. "Foldings of G-trees."
2273:, vol. 76 (2008), no. 1, pp. 159–168
1407:Arboreal group theory (Berkeley, CA, 1988)
1041:"How not to prove the Poincaré conjecture"
639:over a finite group (that is, in terms of
191:(July 22, 1935 – November 24, 2008) was a
29:
18:
2706:
2631:"On the Grigorchuk–Kurchanov conjecture."
2594:
2592:
2438:Group theory from a geometrical viewpoint
2415:Group theory from a geometrical viewpoint
2140:, vol. 248 (2002), no. 2, 608–668
1092:
939:and they have also found applications in
904:using combinatorial methods, such as the
830:
791:
782:
762:
732:
706:
678:
663:
575:
569:
548:
542:
521:
515:
496:
495:
487:
468:
467:
465:
444:
438:
405:
399:
2462:(3) 65 (1992), no. 1, pp. 199–224.
2374:, 1, Geom. Topol. Publ., Coventry, 1998.
313:Mathematical Sciences Research Institute
287:International Congress of Mathematicians
2510:3-manifolds which fiber over a surface.
1910:Groups of dimension 1 are locally free.
1881:(2), vol. 88 (1968), pp. 312–334.
1865:, vol. 14 (2007), no. 4, 547–558.
1624:MacTutor History of Mathematics Archive
1490:
1488:
1486:
1484:
1482:
1480:
1478:
1474:
757:admits a splitting as an HNN extension
622:Stallings' theorem about ends of groups
379:in 1982, it was shown that 4-space has
195:known for his seminal contributions to
2561:, vol. 10 (2006), pp. 2431–2499
2475:, 319. Springer-Verlag, Berlin, 1999.
2130:
2128:
2003:Martin J. Dunwoody and E. L. Swenson.
1569:, New Haven, Conn.–London, 1971.
960:fundamental groups of graphs of groups
221:Stallings theorem about ends of groups
105:Stallings theorem about ends of groups
2021:G. Peter Scott, and Gadde A. Swarup.
1740:Queen Mary College Mathematical Notes
1557:
1555:
1520:
1518:
1351:(1983), "Topology of finite graphs",
1264:(2), Annals of Mathematics: 312–334,
219:and a proof, in a 1971 paper, of the
7:
2786:21st-century American mathematicians
2781:20th-century American mathematicians
2636:107 (2002), no. 4, pp. 451–461
1849:Martin R. Bridson, and James Howie.
1831:Martin R. Bridson, and James Howie.
1822:, vol. 92 (2002), pp. 95–103.
1672:, vol. 66 (1960), pp. 485–488.
1652:University of California at Berkeley
205:University of California at Berkeley
147:University of California at Berkeley
2586:, vol. 40 (1966), pp. 153–160
2579:2Fibering manifolds over a circle."
2530:, vol. 215 (1975), pp. 35–45.
2515:, vol. 94 (1972), pp. 189–205
2456:Jon Corson. "Complexes of groups."
1991:Journal of Pure and Applied Algebra
1892:Applications of Categorical Algebra
1579:Frank Nelson Cole Prize in Algebra.
1525:Chang, Kenneth (January 18, 2009),
954:for approximating group actions on
601:for cubical complexes developed by
2157:, vol. 94 (2002), pp. 33–43.
989:Among Stallings' contributions to
612:Stallings' most famous theorem in
302:Frank Nelson Cole Prize in Algebra
238:Stallings received his B.Sc. from
119:Frank Nelson Cole Prize in Algebra
14:
2583:Commentarii Mathematici Helvetici
1932:2 (1982), no. 1, pp. 15–23.
1837:Geometric and Functional Analysis
1512:Volume 3, Issue 4; November 2002.
966:context by other mathematicians.
503:{\displaystyle 1\in \mathbb {Z} }
383:, in fact uncountably many such.
2372:Geometry and Topology Monographs
1394:, with over 100 recent citations
977:(a higher-dimensional analog of
2811:People from Morrilton, Arkansas
2629:Tullio Ceccherini-Silberstein.
2513:American Journal of Mathematics
1973:American Journal of Mathematics
1705:American Journal of Mathematics
1216:American Journal of Mathematics
1094:10.1090/s0002-9904-1960-10511-3
394:and, moreover, not of the type
260:Alfred P. Sloan Research fellow
246:in 1959 under the direction of
2311:Pacific Journal of Mathematics
2072:Revista Matemática Complutense
2036:Pacific Journal of Mathematics
2005:"The algebraic torus theorem."
783:
341:(particularly the topology of
1:
2796:University of Arkansas alumni
2730:Mathematics Genealogy Project
2541:Topology and its Applications
2248:American Mathematical Society
2024:An algebraic annulus theorem.
1896:American Mathematical Society
1863:Mathematical Research Letters
1582:American Mathematical Society
1547:Group theory and 3-manifolds.
1334:American Mathematical Society
1077:"Polyhedral homotopy spheres"
1013:, such that this subgroup is
997:. The theorem states that if
993:, the most well-known is the
690:{\displaystyle G=A\ast _{C}B}
306:American Mathematical Society
109:Stallings graphs and automata
2816:Mathematicians from Arkansas
2090:"Topology of finite graphs."
1666:Polyhedral homotopy spheres.
1536:. Accessed January 26, 2009.
1415:10.1007/978-1-4612-3142-4_14
1196:10.1016/0021-8693(65)90017-7
1047:reformulation of the famous
475:{\displaystyle \mathbb {Z} }
2801:Princeton University alumni
2112:Combinatorial Group Theory.
1654:. Accessed December 4, 2008
995:Stallings fibration theorem
421:, that is, not admitting a
2837:
2741:Remembering John Stallings
1039:A 1965 paper of Stallings
902:combinatorial group theory
624:. Stallings proved that a
482:of integers that sends to
329:Mathematical contributions
2402:SIAM Journal on Computing
1134:10.1017/S0305004100036756
1001:is a compact irreducible
906:Schreier rewriting method
850:{\displaystyle K,L\leq H}
189:John Robert Stallings Jr.
182:
125:
28:
2349:Inventiones Mathematicae
2250:, Providence, RI, 2002;
2170:Inventiones Mathematicae
2149:J. Meakin, and P. Weil.
2094:Inventiones Mathematicae
2009:Inventiones Mathematicae
1948:Groups acting on graphs.
1898:, Providence, R.I, 1970.
1762:Inventiones Mathematicae
1629:University of St Andrews
1354:Inventiones Mathematicae
930:Hanna Neumann conjecture
922:Stallings subgroup graph
916:that also used a simple
883:CAT(0) cubical complexes
649:finitely generated group
633:amalgamated free product
626:finitely generated group
388:finitely presented group
381:exotic smooth structures
339:low-dimensional topology
2634:Manuscripta Mathematica
2558:Geometry & Topology
2218:Journal of Group Theory
1603:, atlas-conferences.com
910:Nielsen transformations
746:{\displaystyle C\neq B}
720:{\displaystyle C\neq A}
590:{\displaystyle F_{n+1}}
300:Stallings received the
258:2005. Stallings was an
35:2006 photo of Stallings
2821:Sloan Research Fellows
878:geometric group theory
851:
819:
747:
721:
691:
591:
558:
531:
504:
476:
460:to the additive group
454:
415:
335:geometric group theory
325:on November 24, 2008.
276:geometric group theory
240:University of Arkansas
209:geometric group theory
197:geometric group theory
86:University of Arkansas
16:American mathematician
2527:Mathematische Annalen
2325:Arboreal group theory
2230:10.1515/jgth.2001.012
1879:Annals of Mathematics
1783:10.1007/s002220050168
1690:Annals of Mathematics
1567:Yale University Press
1301:Yale University Press
1257:Annals of Mathematics
1055:(see, for example,).
937:finite-state automata
914:covering space theory
852:
820:
748:
722:
692:
592:
559:
557:{\displaystyle F_{n}}
532:
530:{\displaystyle F_{2}}
505:
477:
455:
453:{\displaystyle F_{2}}
416:
414:{\displaystyle F_{3}}
2776:American topologists
2109:and Paul E. Schupp.
1927:"Cutting up graphs."
1615:Robertson, Edmund F.
1510:All things academic.
1021:by this subgroup is
900:has been studied in
829:
761:
731:
705:
662:
568:
541:
514:
486:
464:
437:
398:
278:and the topology of
255:University of Oxford
244:Princeton University
211:and the topology of
90:Princeton University
74:Berkeley, California
2651:Russian Mathematics
2396:Yuri Gurevich, and
2214:Formanek, Edward W.
2183:1994InMat.117..373D
2155:Geometriae Dedicata
2088:John R. Stallings.
1907:John R. Stallings.
1874:John R. Stallings.
1819:Geometriae Dedicata
1775:1997InMat.129..445B
1613:O'Connor, John J.;
1545:John R. Stallings.
1367:1983InMat..71..551S
1167:, pp. 95–100,
1126:1962PCPS...58..481S
1053:Poincaré conjecture
1049:Poincaré conjecture
991:3-manifold topology
975:complexes of groups
318:Geometriae Dedicata
233:Morrilton, Arkansas
201:3-manifold topology
55:Morrilton, Arkansas
2737:of John Stallings.
2690:. 12 January 2009.
2191:10.1007/BF01232249
2137:Journal of Algebra
2030:2007-07-15 at the
1943:Martin J. Dunwoody
1923:Martin J. Dunwoody
1858:2008-07-05 at the
1744:Queen Mary College
1646:2008-12-28 at the
1599:2008-09-06 at the
1532:The New York Times
1440:Stallings, John R.
1399:Stallings, John R.
1375:10.1007/BF02095993
1349:Stallings, John R.
1336:, pp. 55–60,
1326:Stallings, John R.
1293:Stallings, John R.
1252:Stallings, John R.
1184:Journal of Algebra
1180:Stallings, John R.
1157:Stallings, John R.
1110:Stallings, John R.
1073:Stallings, John R.
1017:and such that the
1015:finitely generated
971:triangle of groups
847:
815:
743:
717:
697:, where the group
687:
587:
554:
527:
500:
472:
450:
411:
272:J. Hyam Rubinstein
268:Stephen M. Gersten
177:J. Hyam Rubinstein
173:Stephen M. Gersten
2726:John R. Stallings
2367:Folding sequences
2121:978-3-540-41158-1
1985:Gadde A. Swarup.
1941:Warren Dicks and
1811:Martin R. Bridson
1453:978-981-02-0442-6
1424:978-0-387-97518-4
1401:(1991), "Folding
1310:978-0-300-01397-9
1260:, Second Series,
1007:fundamental group
979:Bass–Serre theory
964:Bass–Serre theory
952:Bass–Serre theory
926:Stallings folding
641:Bass–Serre theory
423:classifying space
186:
185:
165:Doctoral students
127:Scientific career
66:November 24, 2008
23:John R. Stallings
2828:
2713:
2712:
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2691:
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2677:, 9782553013997.
2663:Valentin Poénaru
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1753:
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1663:John Stallings.
1661:
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1619:"John Stallings"
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945:computer science
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373:Michael Freedman
154:Doctoral advisor
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2771:Group theorists
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2344:Mladen Bestvina
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2271:Semigroup Forum
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2107:Roger C. Lyndon
2105:
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2048:Michah Sageev.
2047:
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2032:Wayback Machine
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1229:10.2307/2373106
1211:Stallings, John
1209:
1178:
1155:
1108:
1071:
1068:
1045:group-theoretic
1034:Haken manifolds
1023:infinite cyclic
1011:normal subgroup
983:André Haefliger
918:graph-theoretic
827:
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377:Simon Donaldson
331:
323:prostate cancer
295:Yale University
229:
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2720:External links
2718:
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2679:
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2611:Robert Myers.
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2224:(2): 113–151.
2204:
2177:(3): 373–389.
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2124:
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2068:Wall, C. T. C.
2059:
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2014:
1996:
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1960:
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1120:(3): 481–488,
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1067:
1066:Selected works
1064:
1019:quotient group
943:theory and in
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2575:Jerome Levine
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2708:math/9306203
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2500:
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2238:
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2174:
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2150:
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2111:
2102:
2092:
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2044:
2034:
2023:
2017:
2007:
1999:
1989:
1981:
1971:
1963:
1947:
1937:
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921:
891:
867:
862:
754:
698:
655:
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628:
614:group theory
611:
607:limit groups
599:Morse theory
426:
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368:
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316:
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284:
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188:
187:
143:Institutions
126:
68:(2008-11-24)
2766:2008 deaths
2761:1935 births
2398:Paul Schupp
2078:(1): 5–101.
1498:UC Berkeley
1060:Interlingua
1009:contains a
898:free groups
874:free groups
857:are finite
343:3-manifolds
280:3-manifolds
264:Marc Culler
213:3-manifolds
169:Marc Culler
137:Mathematics
2755:Categories
2600:R. H. Bing
1003:3-manifold
432:free group
47:1935-07-22
2735:home page
2199:121902432
1799:120422255
1405:-trees",
1150:120418488
941:semigroup
894:subgroups
859:subgroups
842:≤
813:⟩
793:−
771:⟨
738:≠
712:≠
676:∗
635:or as an
493:∈
308:in 1970.
304:from the
297:in 1969.
248:Ralph Fox
227:Biography
159:Ralph Fox
99:proof of
2028:Archived
1856:Archived
1644:Archived
1597:Archived
1391:16643207
1295:(1971),
1075:(1960),
2728:at the
2179:Bibcode
1791:1465330
1771:Bibcode
1726:2373106
1462:1170374
1433:1105341
1383:0695906
1363:Bibcode
1342:0520522
1319:0415622
1286:0228573
1278:1970577
1245:0158917
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825:where
270:, and
133:Fields
121:(1971)
115:Awards
76:, U.S.
57:, U.S.
2703:arXiv
2195:S2CID
1795:S2CID
1722:JSTOR
1469:Notes
1387:S2CID
1274:JSTOR
1233:JSTOR
1146:S2CID
956:trees
870:order
753:, or
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