1875:
1658:
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1933:
1906:
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31:
970:. In dimension four, in marked contrast with lower dimensions, topological and smooth manifolds are quite different. There exist some topological 4-manifolds that admit no smooth structure and even if there exists a smooth structure it need not be unique (i.e. there are smooth 4-manifolds that are
564:
Phenomena in three dimensions can be strikingly different from phenomena in other dimensions, and so there is a prevalence of very specialized techniques that do not generalize to dimensions greater than three. This special role has led to the discovery of close connections to a diversity of other
1179:
There are compact 4-dimensional topological manifolds that are not homeomorphic to any simplicial complex. In dimension at least 5 the existence of topological manifolds not homeomorphic to a simplicial complex was an open problem. In 2013, Ciprian
Manolescu posted a preprint on the ArXiv showing
867:
Its thick-thin decomposition has a thin part consisting of tubular neighborhoods of closed geodesics and/or ends that are the product of a
Euclidean surface and the closed half-ray. The manifold is of finite volume if and only if its thick part is compact. In this case, the ends are of the form
1103:
There are several fundamental theorems about manifolds that can be proved by low-dimensional methods in dimensions at most 3, and by completely different high-dimensional methods in dimension at least 5, but which are false in four dimensions. Here are some examples:
1172:
holds for cobordisms provided that neither the cobordism nor its boundary has dimension 4. It can fail if the boundary of the cobordism has dimension 4 (as shown by
Donaldson). If the cobordism has dimension 4, then it is unknown whether the h-cobordism theorem
1127:
In any dimension other than 4, a compact topological manifold has only a finite number of essentially distinct PL or smooth structures. In dimension 4, compact manifolds can have a countable infinite number of non-diffeomorphic smooth
110:
in five or more dimensions made dimensions three and four seem the hardest; and indeed they required new methods, while the freedom of higher dimensions meant that questions could be reduced to computational methods available in
630:. While inspired by knots that appear in daily life in shoelaces and rope, a mathematician's knot differs in that the ends are joined together so that it cannot be undone. In mathematical language, a knot is an
1124:) vanishes. In dimension 3 and lower, every topological manifold admits an essentially unique PL structure. In dimension 4 there are many examples with vanishing Kirby–Siebenmann invariant but no PL structure.
499:. This classifies Riemannian surfaces as elliptic (positively curved—rather, admitting a constant positively curved metric), parabolic (flat), and hyperbolic (negatively curved) according to their
771:
561:, and smooth categories are all equivalent in three dimensions, so little distinction is made in whether we are dealing with say, topological 3-manifolds, or smooth 3-manifolds.
1112:
provides the obstruction to the existence of a PL structure; in other words a compact topological manifold has a PL structure if and only if its Kirby–Siebenmann invariant in H(
342:
The surfaces in the third family are nonorientable. The Euler characteristic of the real projective plane is 1, and in general the Euler characteristic of the connected sum of
122:, formulated in the late 1970s, offered a framework that suggested geometry and topology were closely intertwined in low dimensions, and Thurston's proof of geometrization for
1189:
There are several theorems that in effect state that many of the most basic tools used to study high-dimensional manifolds do not apply to low-dimensional manifolds, such as:
1176:
A topological manifold of dimension not equal to 4 has a handlebody decomposition. Manifolds of dimension 4 have a handlebody decomposition if and only if they are smoothable.
795:, in which the group operation is 'do the first braid on a set of strings, and then follow it with a second on the twisted strings'. Such groups may be described by explicit
1165:
has been proved for all dimensions other than 4, but it is not known whether it is true in 4 dimensions (it is equivalent to the smooth
Poincaré conjecture in 4 dimensions).
920:). In three dimensions, it is not always possible to assign a single geometry to a whole topological space. Instead, the geometrization conjecture states that every closed
438:
structure and a wealth of natural metrics. The underlying topological space of TeichmĂĽller space was studied by Fricke, and the TeichmĂĽller metric on it was introduced by
306:
270:
1936:
1376:
658:); these transformations correspond to manipulations of a knotted string that do not involve cutting the string or passing the string through itself.
886:
134:
in the early 1980s not only led knot theory in new directions but gave rise to still mysterious connections between low-dimensional topology and
924:
can be decomposed in a canonical way into pieces that each have one of eight types of geometric structure. The conjecture was proposed by
1570:
1957:
1924:
1919:
1281:
816:
90:. It may also be used to refer to the study of topological spaces of dimension 1, though this is more typically considered part of
1463:
1426:
1206:
Any closed 3-manifold is the boundary of a 4-manifold. This theorem is due independently to several people: it follows from the
586:
1914:
1109:
598:
1816:
857:
1180:
that there are manifolds in each dimension greater than or equal to 5, that are not homeomorphic to a simplicial complex.
1045:
1071:—were already known to exist, although the question of the existence of such structures for the particular case of the
1962:
543:
1257:
102:
A number of advances starting in the 1960s had the effect of emphasising low dimensions in topology. The solution by
1824:
721:
183:. The most familiar examples are those that arise as the boundaries of solid objects in ordinary three-dimensional
316:. It is convenient to combine the two families by regarding the sphere as the connected sum of 0 tori. The number
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119:
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796:
708:
507:
1844:
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1154:
933:
894:
570:
455:
216:
107:
1686:
1613:
1336:
834:
828:
646:(since we're using topology, a circle isn't bound to the classical geometric concept, but to all of its
476:
279:
1874:
1301:
650:). Two mathematical knots are equivalent if one can be transformed into the other via a deformation of
439:
1834:
1786:
1760:
1608:
1200:
959:
692:
582:
362:
325:
222:
180:
135:
1885:
1681:
1169:
917:
849:
792:
574:
143:
893:
each have a unique geometric structure that can be associated with them. It is an analogue of the
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1829:
1750:
1740:
1618:
1598:
1215:
1211:
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913:
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203:
191:
172:
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151:
87:
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157:
Overall, this progress has led to better integration of the field into the rest of mathematics.
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1733:
1691:
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902:
853:
469:
386:
139:
131:
116:
91:
1514:
1476:
1439:
1399:
1357:
1317:
1157:
is known in all dimensions other than 4 (it is usually false in dimensions at least 7; see
1706:
1701:
1510:
1472:
1454:
1435:
1395:
1353:
1313:
1253:
1241:
1057:
1041:
1030:
905:
661:
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639:
500:
472:
413:
225:
184:
176:
671:
is the three-dimensional space surrounding the knot. To make this precise, suppose that
1796:
1728:
1196:
1040:, by using the contrast between Freedman's theorems about topological 4-manifolds, and
1026:
861:
842:
594:
488:
432:
328:
2 and 0, respectively, and in general the Euler characteristic of the connected sum of
123:
112:
126:
utilized a variety of tools from previously only weakly linked areas of mathematics.
17:
1951:
1806:
1716:
1696:
1542:
1245:
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39:
35:
1219:
1535:
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1417:
791:
concept, and some generalizations. The idea is that braids can be organized into
1889:
1801:
1374:(1982), "Three-dimensional manifolds, Kleinian groups and hyperbolic geometry",
1162:
808:
704:
623:
614:
566:
461:
368:
83:
79:
51:
43:
30:
1745:
1676:
1635:
1506:
1331:
1304:(1940), "Extremale quasikonforme Abbildungen und quadratische Differentiale",
1075:
remained open (and still remains open to this day). For any positive integer
949:
921:
838:
811:. Braid groups may also be given a deeper mathematical interpretation: as the
800:
526:
147:
75:
71:
1770:
1268:
is known to have exactly one smooth structure up to diffeomorphism provided
1230:
1223:
1144:
1002:
986:
665:
631:
480:
199:
67:
1260:
to show there exists a continuum of non-diffeomorphic smooth structures on
1755:
1723:
1672:
1579:
1207:
1072:
781:
684:
601:. 3-manifold theory is considered a part of low-dimensional topology or
511:
435:
425:
398:
63:
59:
228:
surface is homeomorphic to some member of one of these three families:
142:
announced a proof of the three-dimensional
Poincaré conjecture, using
807:). For an elementary treatment along these lines, see the article on
784:
635:
514:
1349:
872:. Knot complements are the most commonly studied cusped manifolds.
788:
243:
29:
1185:
A few typical theorems that distinguish low-dimensional topology
1552:
1495:
Mathematical
Proceedings of the Cambridge Philosophical Society
1493:(1962), "The piecewise-linear structure of Euclidean space",
852:-1. In other words, it is the quotient of three-dimensional
664:
are frequently-studied 3-manifolds. The knot complement of a
517:
of the plane to arbitrary simply connected
Riemann surfaces.
416:
where a 'marking' is an isotopy class of homeomorphisms from
1548:
1143:
has an uncountable number of exotic smooth structures; see
856:
by a subgroup of hyperbolic isometries acting freely and
202:
in three-dimensional
Euclidean space without introducing
66:, or more generally topological spaces, of four or fewer
1545: – lists of homepages, conferences, etc.
1538: – gzipped postscript file (1.4 MB)
1079:
other than 4, there are no exotic smooth structures on
1036:. The first examples were found in the early 1980s by
932:), and implies several other conjectures, such as the
745:
506:
The uniformization theorem is a generalization of the
1459:"Gauge theory on asymptotically periodic 4-manifolds"
1203:
of a 3-manifold is the obstruction to orientability.
981:
4-manifolds are of importance in physics because, in
724:
288:
252:
194:. On the other hand, there are surfaces, such as the
412:
may be regarded as an isomorphism class of 'marked'
70:. Representative topics are the structure theory of
1815:
1779:
1665:
1586:
1195:states that an orientable 3-manifold has a trivial
1044:'s theorems about smooth 4-manifolds. There is a
765:
300:
264:
46:is an important part of low-dimensional topology.
868:torus cross the closed half-ray and are called
1063:Prior to this construction, non-diffeomorphic
324:of the surface. The sphere and the torus have
1564:
1377:Bulletin of the American Mathematical Society
1087:≠4 then any smooth manifold homeomorphic to
766:{\displaystyle X_{K}=M-{\mbox{interior}}(N).}
34:A three-dimensional depiction of a thickened
8:
1248:. It has since been elaborated by Freedman,
443:
312:The surfaces in the first two families are
1932:
1905:
1571:
1557:
1549:
1099:Other special phenomena in four dimensions
1389:
1218:of the 3-manifold. It also follows from
744:
729:
723:
287:
251:
929:
1306:Abh. Preuss. Akad. Wiss. Math.-Nat. Kl.
1293:
908:can be given one of three geometries (
889:states that certain three-dimensional
876:Poincaré conjecture and geometrization
479:to one of the three domains: the open
1139:can have an exotic smooth structure.
804:
7:
1536:Problems in Low-Dimensional Topology
887:Thurston's geometrization conjecture
150:, an idea belonging to the field of
86:. This can be regarded as a part of
707:. The knot complement is then the
1236:. This was originally observed by
538:is a 3-manifold if every point in
431:TeichmĂĽller space has a canonical
25:
1543:links to low dimensional topology
1282:List of geometric topology topics
1931:
1904:
1894:
1884:
1873:
1863:
1862:
1656:
1464:Journal of Differential Geometry
1427:Journal of Differential Geometry
1199:. Stated another way, the only
1108:In dimensions other than 4, the
587:topological quantum field theory
424:. The TeichmĂĽller space is the
385:, is a space that parameterizes
381:of a (real) topological surface
1391:10.1090/S0273-0979-1982-15003-0
1161:). The Poincaré conjecture for
428:of the (Riemann) moduli space.
320:of tori involved is called the
190:—for example, the surface of a
780:. Braid theory is an abstract
757:
751:
675:is a knot in a three-manifold
599:partial differential equations
1:
510:from proper simply connected
1334:(1947), "Theory of braids",
1231:exotic smooth structures on
491:. In particular it admits a
1153:The solution to the smooth
1131:Four is the only dimension
426:universal covering orbifold
1979:
1825:Banach fixed-point theorem
1226:ring of closed manifolds.
1110:Kirby–Siebenmann invariant
1000:
947:
901:, which states that every
879:
826:
612:
524:
453:
360:
210:Classification of surfaces
164:
1858:
1654:
1507:10.1017/S0305004100036756
1050:differentiable structures
882:Geometrization conjecture
654:upon itself (known as an
120:geometrization conjecture
1958:Low-dimensional topology
1056:, as was shown first by
938:elliptization conjecture
858:properly discontinuously
56:low-dimensional topology
1422:'s and other anomalies"
1240:, based on the work of
1019:differentiable manifold
966:is a 4-manifold with a
508:Riemann mapping theorem
301:{\displaystyle k\geq 1}
265:{\displaystyle g\geq 1}
206:or self-intersections.
1880:Mathematics portal
1780:Metrics and properties
1766:Second-countable space
1455:Taubes, Clifford Henry
1222:'s computation of the
895:uniformization theorem
823:Hyperbolic 3-manifolds
787:studying the everyday
767:
571:geometric group theory
477:conformally equivalent
466:uniformization theorem
456:Uniformization theorem
450:Uniformization theorem
440:Oswald TeichmĂĽller
403:identity homeomorphism
302:
280:real projective planes
266:
217:classification theorem
47:
18:4-dimensional topology
1337:Annals of Mathematics
1083:; in other words, if
1048:of non-diffeomorphic
835:hyperbolic 3-manifold
829:Hyperbolic 3-manifold
768:
609:Knot and braid theory
326:Euler characteristics
303:
275:the connected sum of
267:
33:
1835:Invariance of domain
1787:Euler characteristic
1761:Bundle (mathematics)
1372:Thurston, William P.
1201:characteristic class
1091:is diffeomorphic to
960:topological manifold
926:William Thurston
897:for two-dimensional
817:configuration spaces
722:
693:tubular neighborhood
393:up to the action of
286:
250:
181:topological manifold
136:mathematical physics
1845:Tychonoff's theorem
1840:Poincaré conjecture
1594:General (point-set)
1302:TeichmĂĽller, Oswald
1170:h-cobordism theorem
1155:Poincaré conjecture
958:is a 4-dimensional
934:Poincaré conjecture
850:sectional curvature
776:A related topic is
575:hyperbolic geometry
144:Richard S. Hamilton
130:' discovery of the
108:Poincaré conjecture
38:, the simplest non-
1963:Geometric topology
1830:De Rham cohomology
1751:Polyhedral complex
1741:Simplicial complex
1541:Mark Brittenham's
1216:Heegaard splitting
1193:Steenrod's theorem
983:General Relativity
891:topological spaces
799:, as was shown by
763:
749:
628:mathematical knots
603:geometric topology
583:TeichmĂĽller theory
497:constant curvature
387:complex structures
298:
262:
219:of closed surfaces
167:surface (topology)
152:geometric analysis
106:, in 1961, of the
88:geometric topology
48:
27:Branch of topology
1945:
1944:
1734:fundamental group
1488:Corollary 5.2 of
1340:, Second Series,
1229:The existence of
1065:smooth structures
991:pseudo-Riemannian
964:smooth 4-manifold
846:Riemannian metric
813:fundamental group
748:
638:in 3-dimensional
557:The topological,
552:Euclidean 3-space
533:topological space
493:Riemannian metric
373:TeichmĂĽller space
363:TeichmĂĽller space
357:TeichmĂĽller space
198:, that cannot be
58:is the branch of
16:(Redirected from
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1238:Michael Freedman
1038:Michael Freedman
989:is modeled as a
968:smooth structure
903:simply-connected
854:hyperbolic space
841:equipped with a
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769:
764:
750:
746:
734:
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662:Knot complements
626:is the study of
565:fields, such as
559:piecewise-linear
521:Three dimensions
470:simply connected
468:says that every
414:Riemann surfaces
405:. Each point in
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221:states that any
140:Grigori Perelman
132:Jones polynomial
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1452:Theorem 1.1 of
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1350:10.2307/1969218
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1258:Laurence Taylor
1254:Clifford Taubes
1242:Simon Donaldson
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1058:Clifford Taubes
1042:Simon Donaldson
1031:Euclidean space
1008:
999:
952:
946:
944:Four dimensions
936:and Thurston's
906:Riemann surface
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656:ambient isotopy
640:Euclidean space
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501:universal cover
473:Riemann surface
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1526:External links
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1481:
1471:(3): 363–430,
1445:
1434:(2): 317–328,
1418:"Three exotic
1405:
1384:(3): 357–381,
1380:, New Series,
1363:
1323:
1292:
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1284:
1277:
1274:
1214:theorem via a
1197:tangent bundle
1186:
1183:
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1097:
1069:exotic spheres
1001:Main article:
998:
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948:Main article:
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880:Main article:
877:
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862:Kleinian model
827:Main article:
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801:Emil Artin
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648:homeomorphisms
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595:Floer homology
525:Main article:
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489:Riemann sphere
454:Main article:
451:
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395:homeomorphisms
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361:Main article:
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165:Main article:
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161:Two dimensions
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113:surgery theory
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1605:
1604:Combinatorial
1602:
1600:
1597:
1595:
1592:
1591:
1589:
1585:
1581:
1574:
1569:
1567:
1562:
1560:
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1533:
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1496:
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1482:
1478:
1474:
1470:
1466:
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1456:
1449:
1446:
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1437:
1433:
1429:
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1415:
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1397:
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1387:
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1379:
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1373:
1367:
1364:
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1339:
1338:
1333:
1327:
1324:
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1307:
1303:
1297:
1294:
1287:
1283:
1280:
1279:
1275:
1273:
1271:
1267:
1264:. Meanwhile,
1263:
1259:
1255:
1251:
1247:
1246:Andrew Casson
1243:
1239:
1235:
1234:
1227:
1225:
1221:
1217:
1213:
1209:
1204:
1202:
1198:
1194:
1190:
1184:
1178:
1175:
1171:
1167:
1164:
1160:
1159:exotic sphere
1156:
1152:
1149:
1148:
1142:
1138:
1134:
1130:
1126:
1123:
1119:
1115:
1111:
1107:
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1105:
1098:
1096:
1094:
1090:
1086:
1082:
1078:
1074:
1070:
1066:
1061:
1059:
1055:
1051:
1047:
1043:
1039:
1035:
1032:
1028:
1027:diffeomorphic
1024:
1020:
1016:
1013:
1007:
1006:
996:
994:
992:
988:
984:
979:
977:
976:diffeomorphic
973:
969:
965:
961:
957:
951:
943:
941:
939:
935:
931:
927:
923:
919:
915:
911:
907:
904:
900:
896:
892:
888:
883:
875:
873:
871:
865:
863:
859:
855:
851:
847:
844:
840:
836:
830:
822:
820:
818:
814:
810:
806:
802:
798:
797:presentations
794:
790:
786:
783:
779:
760:
754:
741:
738:
735:
730:
726:
718:
717:
716:
714:
710:
706:
702:
698:
694:
690:
686:
682:
679:(most often,
678:
674:
670:
667:
663:
659:
657:
653:
649:
645:
641:
637:
633:
629:
625:
620:
616:
608:
606:
604:
600:
596:
592:
588:
584:
580:
579:number theory
576:
572:
568:
562:
560:
555:
553:
549:
545:
544:neighbourhood
541:
537:
534:
528:
520:
518:
516:
513:
509:
504:
502:
498:
494:
490:
486:
485:complex plane
482:
478:
474:
471:
467:
463:
457:
449:
447:
445:
441:
437:
434:
429:
427:
423:
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396:
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388:
384:
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370:
364:
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345:
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331:
327:
323:
319:
315:
295:
292:
289:
281:
278:
274:
259:
256:
253:
245:
242:
238:
237:connected sum
234:
231:
230:
229:
227:
224:
220:
218:
209:
207:
205:
204:singularities
201:
197:
193:
189:
186:
182:
178:
174:
168:
160:
158:
155:
153:
149:
145:
141:
137:
133:
129:
128:Vaughan Jones
125:
121:
118:
114:
109:
105:
104:Stephen Smale
97:
95:
93:
89:
85:
81:
77:
73:
69:
65:
62:that studies
61:
57:
53:
45:
41:
37:
32:
19:
1937:Publications
1802:Chern number
1792:Betti number
1675: /
1666:Key concepts
1623:
1614:Differential
1498:
1494:
1484:
1468:
1462:
1448:
1431:
1425:
1419:
1408:
1381:
1375:
1366:
1341:
1335:
1326:
1309:
1305:
1296:
1269:
1265:
1261:
1250:Robert Gompf
1232:
1228:
1205:
1192:
1191:
1188:
1163:PL manifolds
1146:
1140:
1136:
1132:
1121:
1117:
1113:
1102:
1092:
1088:
1084:
1080:
1076:
1062:
1053:
1033:
1023:homeomorphic
1014:
1011:
1009:
1004:
993:4-manifold.
980:
972:homeomorphic
963:
955:
953:
885:
869:
866:
860:. See also
848:of constant
832:
809:braid groups
778:braid theory
775:
712:
700:
696:
688:
680:
676:
672:
668:
660:
651:
643:
622:
619:Braid theory
591:gauge theory
563:
556:
548:homeomorphic
539:
535:
530:
505:
465:
459:
430:
421:
417:
406:
390:
382:
375:
372:
366:
349:
343:
341:
335:
329:
321:
317:
311:
276:
240:
215:
213:
196:Klein bottle
187:
170:
156:
101:
84:braid groups
55:
49:
40:trivial knot
36:trefoil knot
1900:Wikiversity
1817:Key results
1501:: 481–488,
1344:: 101–126,
1312:(22): 197,
1168:The smooth
1128:structures.
1067:on spheres—
815:of certain
705:solid torus
624:Knot theory
615:Knot theory
567:knot theory
462:mathematics
369:mathematics
346:of them is
334:2 − 2
232:the sphere;
138:. In 2002,
80:knot theory
76:4-manifolds
72:3-manifolds
52:mathematics
44:Knot theory
1952:Categories
1746:CW complex
1687:Continuity
1677:Closed set
1636:cohomology
1288:References
1135:for which
956:4-manifold
950:4-manifold
922:3-manifold
918:hyperbolic
839:3-manifold
709:complement
527:3-manifold
348:2 −
314:orientable
148:Ricci flow
117:Thurston's
68:dimensions
1925:geometric
1920:algebraic
1771:Cobordism
1707:Hausdorff
1702:connected
1619:Geometric
1609:Continuum
1599:Algebraic
1532:Rob Kirby
1332:Artin, E.
1224:cobordism
1220:René Thom
1212:Lickorish
1046:continuum
987:spacetime
914:spherical
910:Euclidean
782:geometric
742:−
666:tame knot
632:embedding
487:, or the
481:unit disk
397:that are
293:≥
257:≥
223:connected
64:manifolds
1890:Wikibook
1868:Category
1756:Manifold
1724:Homotopy
1682:Interior
1673:Open set
1631:Homology
1580:Topology
1457:(1987),
1416:(1983),
1276:See also
1073:4-sphere
1025:but not
1021:that is
997:Exotic R
974:but not
899:surfaces
843:complete
747:interior
687:). Let
685:3-sphere
683:is the
546:that is
436:manifold
399:isotopic
332:tori is
200:embedded
60:topology
1915:general
1717:uniform
1697:compact
1648:Digital
1515:0149457
1477:0882829
1440:0710057
1400:0648524
1358:0019087
1318:0003242
1210:–
1145:exotic
1029:to the
1003:Exotic
928: (
803: (
515:subsets
442: (
433:complex
401:to the
173:surface
98:History
1910:Topics
1712:metric
1587:Fields
1513:
1475:
1438:
1398:
1356:
1316:
1173:holds.
1012:exotic
793:groups
785:theory
636:circle
597:, and
542:has a
483:, the
464:, the
371:, the
282:, for
246:, for
226:closed
82:, and
1692:Space
1272:≠4.
1017:is a
916:, or
870:cusps
837:is a
789:braid
703:is a
699:; so
691:be a
634:of a
322:genus
175:is a
1310:1939
1256:and
1244:and
1208:Dehn
962:. A
930:1982
805:1947
617:and
512:open
444:1940
244:tori
235:the
214:The
192:ball
74:and
1534:'s
1503:doi
1386:doi
1346:doi
1052:of
1010:An
978:).
711:of
695:of
577:,
550:to
495:of
475:is
460:In
446:).
420:to
389:on
367:In
239:of
146:'s
115:.
50:In
1954::
1511:MR
1509:,
1499:58
1497:,
1473:MR
1469:25
1467:,
1461:,
1436:MR
1432:18
1430:,
1424:,
1396:MR
1394:,
1354:MR
1352:,
1342:48
1314:MR
1308:,
1252:,
1120:/2
1095:.
1060:.
985:,
954:A
940:.
912:,
864:.
833:A
819:.
715:,
642:,
605:.
593:,
589:,
585:,
581:,
573:,
569:,
554:.
531:A
503:.
353:.
339:.
179:,
171:A
154:.
94:.
78:,
54:,
42:.
1572:e
1565:t
1558:v
1518:.
1505::
1443:.
1420:R
1403:.
1388::
1382:6
1361:.
1348::
1321:.
1270:n
1266:R
1262:R
1233:R
1150:.
1147:R
1141:R
1137:R
1133:n
1122:Z
1118:Z
1116:,
1114:M
1093:R
1089:R
1085:n
1081:R
1077:n
1054:R
1034:R
1015:R
1005:R
761:.
758:)
755:N
752:(
739:M
736:=
731:K
727:X
713:N
701:N
697:K
689:N
681:M
677:M
673:K
669:K
652:R
644:R
540:X
536:X
422:X
418:X
409:X
407:T
391:X
383:X
378:X
376:T
350:k
344:k
336:g
330:g
318:g
308:.
296:1
290:k
277:k
272:;
260:1
254:g
241:g
188:R
20:)
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