498:
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1931:
31:
779:. This gave a conjectural picture of 3-manifolds which indicated that all 3-manifolds admitted a certain kind of geometric decomposition involving eight geometries, now called Thurston model geometries. Hyperbolic geometry is the most prevalent geometry in this picture and also the most complicated. The conjecture was proved by
590:
In fact, Thurston resolved so many outstanding problems in foliation theory in such a short period of time that it led to an exodus from the field, where advisors counselled students against going into foliation theory, because
Thurston was "cleaning out the subject" (see "On Proof and Progress in
896:, an extension of his geometrization theorem to the setting of 3-orbifolds. Two teams of mathematicians around 2000 finally finished their efforts to write down a complete proof, based mostly on Thurston's lectures given in the early 1980s in Princeton. His original proof relied partly on
741:
3-manifolds. These were the first such examples; previously it had been believed that except for certain
Seifert fiber spaces, all irreducible 3-manifolds were Haken. These examples were actually hyperbolic and motivated his next theorem.
767:
due to the length and difficulty of the proof. Complete proofs were not written up until almost 20 years later. The proof involves a number of deep and original insights which have linked many apparently disparate fields to
760:. A particularly important corollary is that many knots and links are in fact hyperbolic. Together with his hyperbolic Dehn surgery theorem, this showed that closed hyperbolic 3-manifolds existed in great abundance.
713:
as the union of two regular ideal hyperbolic tetrahedra whose hyperbolic structures matched up correctly and gave the hyperbolic structure on the figure-eight knot complement. By utilizing
892:
structures naturally arose. Such structures had been studied prior to
Thurston, but his work, particularly the next theorem, would bring them to prominence. In 1981, he announced the
2858:
927:
in 1982 for "revolutioniz study of topology in 2 and 3 dimensions, showing interplay between analysis, topology, and geometry" and "contribut idea that a very large class of closed
107:
556:
429:
During
Thurston's directorship at MSRI, the institute introduced several innovative educational programs that have since become standard for research institutes.
2898:
353:
as a child, causing issues with depth perception. His mother worked with him as a toddler to reconstruct three-dimensional images from two-dimensional ones.
2883:
951:
by the
American Mathematical Society for seminal contribution to research. The citation described his work as having "revolutionized 3-manifold theory".
2843:
560:
2615:
2893:
745:
Thurston proved that in fact most Dehn fillings on a cusped hyperbolic 3-manifold resulted in hyperbolic 3-manifolds. This is his celebrated
2903:
2868:
2863:
1439:
947:. The prize "recognizes an outstanding research book that makes a seminal contribution to the research literature". He was awarded the 2012
1915:
1238:
989:
943:
1423:
1055:. University Lecture Series, 13. American Mathematical Society, Providence, Rhode Island and Providence Plantations, 1998. x+66 pp.
687:
in the mid-to-late 1970s showed that such examples were less atypical than previously believed; in particular their work showed that the
1793:
2077:
1358:
1000:. Edited by Silvio Levy. Princeton Mathematical Series, 35. Princeton University Press, Princeton, New Jersey, 1997. x+311 pp.
1662:
1066:
404:
327:
186:
1963:
1159:
103:
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810:
in the late 1970s and early 1980s. The conjecture states that every finitely generated
Kleinian group is an algebraic limit of
1255:
2878:
2608:
1830:
1273:
389:
198:
725:
in the knot complement. Together with his analysis of deformations of hyperbolic structures, he concluded that all but 10
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1129:
1119:
800:
111:
1149:
1035:
Epstein, David B. A.; Cannon, James W.; Holt, Derek F.; Levy, Silvio V. F.; Paterson, Michael S.; Thurston, William P.
400:
365:
190:
93:
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1935:
1693:
1154:
1060:
1046:
1005:
875:
849:
705:
Inspired by their work, Thurston took a different, more explicit means of exhibiting the hyperbolic structure of the
650:
628:
857:
2601:
1686:
Collected works of
William P. Thurston with commentary. Vol. II. 3-manifolds, complexity and geometric group theory
473:
276:
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2625:
2039:
917:
688:
408:
319:
252:
182:
130:
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964:
853:
632:
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1947:
1386:
1164:
960:
935:
477:
419:
2052:
William
Goldman (U. of Maryland), Collloquium, Department of Mathematics, Howard University, 25 January 2013
730:
680:
540:
on a manifold can be integrated to a foliation (this implies, in particular, that every manifold with zero
385:
202:
140:
959:
Thurston and his first wife, Rachel
Findley, had three children: Dylan, Nathaniel, and Emily. Dylan was a
2783:
1879:
814:
Kleinian groups, and was independently proven by
Ohshika and Namazi–Souto in 2011 and 2012 respectively.
445:
1910:
1731:
349:), a seamstress, and Paul Thurston, an aeronautical engineer. William Thurston suffered from congenital
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2637:
2214:
509:
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1037:
776:
600:
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1968:
838:
804:
300:
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1958:
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842:
753:
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than was previously realised. Prior to Thurston, there were only a handful of known examples of
621:
967:. Thurston had two children with his second wife, Julian Muriel Thurston: Hannah Jade and Liam.
344:
2366:
2197:
1099:
722:
710:
357:
135:
89:
1294:
Laudenbach, François; Papadopoulos, Athanase (2019). "W. P. Thurston and French mathematics".
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1619:
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948:
672:
583:
150:
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1979:
1974:
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938:
893:
811:
541:
396:
315:
194:
1867:
8:
2747:
2717:
2683:
1954:
971:
913:
897:
738:
664:
537:
364:
foundation for topology. Following this, he received a doctorate in mathematics from the
77:
1615:"Realising end invariants by limits of minimally parabolic, geometrically finite groups"
1614:
1462:
684:
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2582:
2535:
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2415:
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412:
323:
178:
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in 1967 as part of its inaugural class. For his undergraduate thesis, he developed an
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1114:
1104:
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1042:
1001:
706:
551:
The construction of a continuous family of smooth, codimension-one foliations on the
418:
Thurston was an early adopter of computing in pure mathematics research. He inspired
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2170:
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1230:
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2701:
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1226:
780:
457:
339:
260:
225:
58:
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1749:
2803:
2711:
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2513:
2486:
2442:
2427:
2307:
2241:
1891:
1089:
792:
699:
695:
691:
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2695:
2508:
2388:
2339:
2295:
2273:
2258:
2187:
1409:
1363:
1134:
1041:. Jones and Bartlett Publishers, Boston, Massachusetts, 1992. xii+330 pp.
807:
757:
734:
718:
714:
579:
567:
453:
437:
433:
280:
256:
240:
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2043:
2026:
2014:
2002:
1990:
1984:
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1560:
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2799:
2751:
2707:
2649:
2518:
2491:
2371:
2356:
2344:
2334:
2312:
2246:
2202:
2107:
1650:
1588:
1542:
1484:
Perelman, Grisha (2003-03-10). "Ricci flow with surgery on three-manifolds".
1144:
575:
369:
296:
230:
1943:
1709:
1533:
1506:
2727:
2665:
2655:
2285:
2124:
2102:
2086:
1642:
1561:"Non-realizability and ending laminations: Proof of the density conjecture"
1437:
Thurston, William P. (April 1994). "On Proof and Progress in Mathematics".
924:
726:
469:
361:
304:
272:
125:
2158:
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2481:
2437:
2175:
1222:
796:
545:
461:
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441:
264:
248:
244:
168:
1075:
497:
2643:
2192:
2153:
1381:
928:
901:
769:
668:
635: in this section. Unsourced material may be challenged and removed.
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268:
145:
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complement. He showed that the figure-eight knot complement could be
2721:
2623:
1633:
1523:
1490:
1453:
1251:
529:
1023:
Three-dimensional manifolds, Kleinian groups and hyperbolic geometry
827:
610:
295:(October 30, 1946 – August 21, 2012) was an American
2807:
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2540:
2055:
1300:
975:
889:
578:
of a manifold is the same whether the group is considered with its
552:
403:
in 1991 to be a professor (1991-1996) and was also director of the
115:
30:
1329:
423:
763:
The hyperbolization theorem for Haken manifolds has been called
1930:
888:
In his work on hyperbolic Dehn surgery, Thurston realized that
209:
1847:
Department mourns loss of friend and colleague, Bill Thurston
663:
His later work, starting around the mid-1970s, revealed that
1359:"William P. Thurston, Theoretical Mathematician, Dies at 65"
1823:
What's Next? The Mathematical Legacy of William P. Thurston
1030:
On the geometry and dynamics of diffeomorphisms of surfaces
1274:"World-renowned mathematician William Thurston dies at 65"
667:
played a far more important role in the general theory of
2859:
Members of the United States National Academy of Sciences
1424:"The Mathematical Legacy of William Thurston (1946–2012)"
1032:. Bull. Amer. Math. Soc. (N.S.) 19 (1988), no. 2, 417–431
384:
After completing his Ph.D., Thurston spent a year at the
1909:
Gabai, David; Kerckhoff, Steve (Coordinating Editors). "
1330:"Institute for Advanced Study: A Community of Scholars"
215:
Foliations of three-manifolds which are circle bundles
1410:"William Thurston – the Mathematics Genealogy Project"
1316:"William Thurston – the Mathematics Genealogy Project"
1293:
1078:. Notices of the AMS 37:7 (September 1990) pp 844–850
803:
from singly degenerate Kleinian surface groups to all
374:
Foliations of Three-Manifolds which are Circle Bundles
2015:"Landau Lectures | Prof. Thurston | Part 3 | 1995/6"
2003:"Landau Lectures | Prof. Thurston | Part 2 | 1995/6"
1991:"Landau Lectures | Prof. Thurston | Part 1 | 1995/6"
1919:, January 2015, Volume 63, Number 1, pp. 31–41.
395:
In 1974, Thurston was appointed a full professor at
1688:. American Mathematical Society. pp. 147–151.
407:(MSRI) from 1992 to 1997. He was on the faculty at
1750:"William P. Thurston Receives 2005 AMS Book Prize"
1025:, Bull. Amer. Math. Soc. (N.S.) 6 (1982), 357–381.
528:His early work, in the early 1970s, was mainly in
1952:
1071:. Bull. Amer. Math. Soc. (N.S.) 30 (1994) 161–177
2820:
2038:
2021:. Hebrew University of Jerusalem. April 8, 2014.
2009:. Hebrew University of Jerusalem. April 8, 2014.
1997:. Hebrew University of Jerusalem. April 8, 2014.
963:participant (1988–90) and is a mathematician at
594:
2027:"The Mystery of 3-Manifolds - William Thurston"
1554:
1552:
998:Three-dimensional geometry and topology. Vol. 1
2899:Institute for Advanced Study visiting scholars
2044:"William Thurston: A Mathematical Perspective"
1376:
1374:
1356:
1221:
679:. The independent and distinct approaches of
532:theory. His more significant results include:
307:in 1982 for his contributions to the study of
2609:
2071:
1440:Bulletin of the American Mathematical Society
1916:Notices of the American Mathematical Society
1839:
1762:
1742:
1549:
1239:Notices of the American Mathematical Society
1217:
1215:
1213:
1211:
1014:. I. Deformation of acylindrical manifolds.
990:The geometry and topology of three-manifolds
1985:Etienne Ghys : La géométrie et la mode
1558:
1504:
1371:
1209:
1207:
1205:
1203:
1201:
1199:
1197:
1195:
1193:
1191:
1051:Eliashberg, Yakov M.; Thurston, William P.
856:. Unsourced material may be challenged and
752:To complete the picture, Thurston proved a
333:
314:Thurston was a professor of mathematics at
2884:University of California, Berkeley faculty
2616:
2602:
2078:
2064:
1608:
1606:
29:
2844:University of California, Berkeley alumni
1732:"Fields Medals and Nevanlinna Prize 1982"
1724:
1632:
1578:
1532:
1522:
1505:Kleiner, Bruce; Lott, John (2008-11-06).
1489:
1452:
1299:
876:Learn how and when to remove this message
651:Learn how and when to remove this message
1820:
1683:
1483:
1436:
1188:
981:
563:and Jacques Vey) takes every real value.
405:Mathematical Sciences Research Institute
328:Mathematical Sciences Research Institute
187:Mathematical Sciences Research Institute
2894:University of California, Davis faculty
1980:Tribute and remembrance page at Cornell
1964:MacTutor History of Mathematics Archive
1612:
1603:
944:Three-dimensional Geometry and Topology
775:Thurston was next led to formulate his
411:from 1996 until 2003, when he moved to
356:He received his bachelor's degree from
2821:
1271:
993:, Princeton lecture notes (1978–1981).
2597:
2059:
2033:. PoincareDuality. November 27, 2011.
1559:Namazi, Hossein; Souto, Juan (2012).
1352:
1350:
1348:
1346:
970:Thurston died on August 21, 2012, in
786:
729:on the figure-eight knot resulted in
591:Mathematics", especially section 6).
390:Massachusetts Institute of Technology
343:
199:Massachusetts Institute of Technology
2904:Mathematicians from Washington, D.C.
2869:21st-century American mathematicians
2864:20th-century American mathematicians
2085:
1430:
1160:Thurston's geometrization conjecture
1068:On proof and progress in mathematics
1012:Hyperbolic structures on 3-manifolds
907:
854:adding citations to reliable sources
821:
633:adding citations to reliable sources
604:
492:
104:Thurston's geometrization conjecture
1880:doi:10.1090/S0273-0979-1994-00481-1
1738:. International Mathematical Union.
817:
698:. This was the first example of a
299:. He was a pioneer in the field of
13:
1903:
1357:Leslie Kaufman (August 23, 2012).
1343:
366:University of California, Berkeley
191:University of California, Berkeley
94:University of California, Berkeley
16:American mathematician (1946–2012)
14:
2915:
1923:
1665:from the original on May 25, 2014
1155:Thurston elliptization conjecture
1018:. (2) 124 (1986), no. 2, 203–246.
2577:
2568:
2567:
1929:
1821:Thurston, Dylan P., ed. (2020).
1782:from the original on 2022-10-09.
1710:"William P. Thurston, 1946–2012"
1382:"William P. Thurston, 1946-2012"
1261:from the original on 2022-10-09.
1231:"William P. Thurston, 1946–2012"
954:
934:In 2005, Thurston won the first
826:
609:
496:
326:. He was also a director of the
2626:Oswald Veblen Prize in Geometry
1852:
1814:
1786:
1702:
1677:
1498:
1477:
1471:10.1090/S0273-0979-1994-00502-6
1150:Thurston's double limit theorem
1130:Nielsen–Thurston classification
1120:Milnor–Thurston kneading theory
931:carry a hyperbolic structure."
918:Oswald Veblen Prize in Geometry
620:needs additional citations for
320:University of California, Davis
183:University of California, Davis
131:Oswald Veblen Prize in Geometry
112:Milnor–Thurston kneading theory
1911:William P. Thurston, 1946–2012
1825:. Princeton University Press.
1416:
1402:
1322:
1308:
1286:
1272:Kelley, Susan (Aug 24, 2012).
1265:
965:Indiana University Bloomington
721:techniques, he classified the
675:of finite volume, such as the
1:
2839:New College of Florida alumni
2035:2010 Clay Research Conference
1948:Mathematics Genealogy Project
1684:Thurston, William P. (2022).
1387:American Mathematical Society
1181:
936:American Mathematical Society
595:The geometrization conjecture
488:
338:William Thurston was born in
108:Thurston's theory of surfaces
2879:Princeton University faculty
1507:"Notes on Perelman's papers"
978:that was diagnosed in 2011.
386:Institute for Advanced Study
203:Institute for Advanced Study
141:National Academy of Sciences
7:
1170:Thurston's orbifold theorem
1165:Thurston's height condition
1125:Misiurewicz–Thurston points
1082:
765:Thurston's Monster Theorem,
570:, he gave a proof that the
483:
432:His Ph.D. students include
392:as an assistant professor.
388:, then another year at the
10:
2920:
2889:Cornell University faculty
2638:Christos Papakyriakopoulos
1975:Thurston's page at Cornell
1613:Ohshika, Ken'ichi (2011).
598:
2632:
2563:
2093:
1888:doi:10.1112/blms/25.6.614
1860:Word Processing in Groups
1580:10.1007/s11511-012-0088-0
1038:Word Processing in Groups
777:geometrization conjecture
601:Geometrization conjecture
379:
286:
236:
224:
208:
174:
164:
157:
121:
99:
85:
66:
40:
28:
21:
1969:University of St Andrews
1770:"AMS prize booklet 2012"
1076:"Mathematical education"
342:, to Margaret Thurston (
334:Early life and education
301:low-dimensional topology
1534:10.2140/gt.2008.12.2587
1511:Geometry & Topology
1110:Hyperbolic Dehn surgery
754:hyperbolization theorem
747:hyperbolic Dehn surgery
723:incompressible surfaces
557:Godbillon–Vey invariant
2854:Differential geometers
1643:10.2140/gt.2011.15.827
1100:Circle packing theorem
923:Thurston received the
912:In 1976, Thurston and
673:hyperbolic 3-manifolds
544:admits a foliation of
136:Alan T. Waterman Award
90:New College of Florida
2790:Fernando Codá Marques
1890:; Richard M. Thomas,
1849:", Cornell University
1620:Geometry and Topology
1074:William P. Thurston,
982:Selected publications
974:, of a sinus mucosal
949:Leroy P. Steele Prize
584:compact-open topology
536:The proof that every
480:, and Jeffrey Weeks.
293:William Paul Thurston
151:Leroy P. Steele Prize
45:William Paul Thurston
2849:American topologists
1955:Robertson, Edmund F.
1938:at Wikimedia Commons
850:improve this section
812:geometrically finite
629:improve this article
542:Euler characteristic
397:Princeton University
316:Princeton University
303:and was awarded the
195:Princeton University
2718:Richard S. Hamilton
2684:James Harris Simons
1953:O'Connor, John J.;
1463:1994math......4236T
1095:Cannon–Thurston map
972:Rochester, New York
914:James Harris Simons
898:Richard S. Hamilton
677:Seifert–Weber space
665:hyperbolic geometry
538:Haefliger structure
426:computing program.
2736:Michael J. Hopkins
2624:Recipients of the
2583:Mathematics portal
2050:. UMD Mathematics.
1959:"William Thurston"
1862:: B. N. Apanasov,
1175:Earthquake theorem
1065:William Thurston,
1028:William Thurston,
1021:William Thurston,
1010:William Thurston,
996:William Thurston,
987:William Thurston,
805:finitely generated
801:density conjecture
787:Density conjecture
508:. You can help by
413:Cornell University
372:, with his thesis
324:Cornell University
179:Cornell University
2816:
2815:
2770:William Minicozzi
2591:
2590:
1934:Media related to
1832:978-0-691-16776-3
1390:. August 22, 2012
1246:(11): 1318–1332.
1227:Kerckhoff, Steven
1140:Orbifold notation
1115:Thurston boundary
1105:Hyperbolic volume
908:Awards and honors
886:
885:
878:
707:figure-eight knot
689:figure-eight knot
661:
660:
653:
580:discrete topology
526:
525:
399:. He returned to
290:
289:
237:Doctoral students
159:Scientific career
2911:
2874:Fields Medalists
2748:Peter Kronheimer
2732:Yakov Eliashberg
2702:Michael Freedman
2678:William Thurston
2618:
2611:
2604:
2595:
2594:
2581:
2571:
2570:
2087:Fields Medalists
2080:
2073:
2066:
2057:
2056:
2051:
2040:Goldman, William
2034:
2022:
2010:
1998:
1971:
1944:William Thurston
1936:William Thurston
1933:
1897:
1872:Gilbert Baumslag
1856:
1850:
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1712:. 30 August 2012
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1600:
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1566:Acta Mathematica
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1526:
1517:(5): 2587–2855.
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1252:10.1090/noti1300
1235:
1219:
894:orbifold theorem
881:
874:
870:
867:
861:
830:
822:
818:Orbifold theorem
781:Grigori Perelman
685:Troels Jørgensen
656:
649:
645:
642:
636:
613:
605:
574:of the group of
561:Claude Godbillon
521:
518:
500:
493:
474:Richard Schwartz
458:Steven Kerckhoff
348:
340:Washington, D.C.
277:Richard Schwartz
261:Steven Kerckhoff
226:Doctoral advisor
220:
80:, New York, U.S.
73:
59:Washington, D.C.
55:October 30, 1946
54:
52:
35:Thurston in 1991
33:
23:William Thurston
19:
18:
2919:
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2914:
2913:
2912:
2910:
2909:
2908:
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2817:
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2804:Simon Donaldson
2712:Clifford Taubes
2672:Dennis Sullivan
2628:
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2112:
2089:
2084:
2042:(May 9, 2013).
2025:
2013:
2001:
1989:
1926:
1906:
1904:Further reading
1901:
1900:
1882:; D. E. Cohen,
1857:
1853:
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1189:
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1179:
1090:Automatic group
1085:
984:
957:
910:
900:'s work on the
882:
871:
865:
862:
847:
831:
820:
808:Kleinian groups
793:Dennis Sullivan
789:
758:Haken manifolds
739:Seifert-fibered
700:hyperbolic knot
657:
646:
640:
637:
626:
614:
603:
597:
522:
516:
513:
506:needs expansion
491:
486:
446:William Goldman
422:to develop the
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336:
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253:William Goldman
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86:Alma mater
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70:August 21, 2012
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2696:Shing-Tung Yau
2692:
2690:Mikhail Gromov
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2075:
2068:
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2054:
2053:
2036:
2023:
2011:
1999:
1987:
1982:
1977:
1972:
1950:
1940:
1939:
1925:
1924:External links
1922:
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1920:
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1627:(2): 827–890.
1602:
1573:(2): 323–395.
1548:
1497:
1476:
1447:(2): 161–177.
1429:
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1401:
1370:
1367:. p. B15.
1364:New York Times
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783:in 2002–2003.
727:Dehn surgeries
719:normal surface
659:
658:
617:
615:
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599:Main article:
596:
593:
588:
587:
576:homeomorphisms
568:John N. Mather
564:
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454:Richard Kenyon
438:Richard Canary
434:Danny Calegari
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257:Richard Kenyon
241:Richard Canary
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100:Known for
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74:(aged 65)
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2536:Duminil-Copin
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1802:
1801:USAMO Archive
1795:
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1737:
1736:mathunion.org
1733:
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1695:9781470468347
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1302:
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1200:
1198:
1196:
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1187:
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1173:
1171:
1168:
1166:
1163:
1161:
1158:
1156:
1153:
1151:
1148:
1146:
1145:Thurston norm
1143:
1141:
1138:
1136:
1133:
1131:
1128:
1126:
1123:
1121:
1118:
1116:
1113:
1111:
1108:
1106:
1103:
1101:
1098:
1096:
1093:
1091:
1088:
1087:
1077:
1073:
1070:
1069:
1064:
1062:
1061:0-8218-0776-5
1058:
1054:
1053:Confoliations
1050:
1048:
1047:0-86720-244-0
1044:
1040:
1039:
1034:
1031:
1027:
1024:
1020:
1017:
1013:
1009:
1007:
1006:0-691-08304-5
1003:
999:
995:
992:
991:
986:
985:
979:
977:
973:
968:
966:
962:
955:Personal life
952:
950:
946:
945:
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926:
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903:
899:
895:
891:
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869:
859:
855:
851:
845:
844:
840:
835:This section
833:
829:
824:
823:
815:
813:
809:
806:
802:
798:
794:
791:Thurston and
784:
782:
778:
773:
771:
766:
761:
759:
755:
750:
748:
743:
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736:
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724:
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693:
690:
686:
682:
678:
674:
670:
666:
655:
652:
644:
634:
630:
624:
623:
618:This section
616:
612:
607:
606:
602:
592:
585:
581:
577:
573:
569:
565:
562:
558:
554:
550:
547:
543:
539:
535:
534:
533:
531:
520:
511:
507:
504:This section
502:
499:
495:
494:
481:
479:
478:William Floyd
475:
471:
467:
463:
459:
455:
451:
447:
443:
439:
435:
430:
427:
425:
421:
420:Jeffrey Weeks
416:
414:
410:
406:
402:
398:
393:
391:
387:
377:
375:
371:
370:Morris Hirsch
367:
363:
359:
354:
352:
346:
341:
331:
329:
325:
321:
317:
312:
310:
306:
302:
298:
297:mathematician
294:
285:
282:
278:
274:
270:
266:
262:
258:
254:
250:
246:
242:
239:
235:
232:
231:Morris Hirsch
229:
227:
223:
216:
213:
211:
207:
204:
200:
196:
192:
188:
184:
180:
177:
173:
170:
167:
163:
160:
156:
152:
147:
142:
137:
132:
127:
124:
120:
117:
113:
109:
105:
102:
98:
95:
91:
88:
84:
79:
69:
65:
60:
43:
39:
32:
27:
20:
2760:Zoltán Szabó
2728:Jeff Cheeger
2677:
2666:Robion Kirby
2656:Morton Brown
2290:
2198:Grothendieck
2047:
2030:
2018:
2006:
1994:
1962:
1914:
1913:" (part 2),
1883:
1875:
1859:
1854:
1841:
1822:
1816:
1804:. Retrieved
1800:
1788:
1764:
1753:. Retrieved
1744:
1735:
1726:
1714:. Retrieved
1704:
1685:
1679:
1667:. Retrieved
1634:math/0504546
1624:
1618:
1570:
1564:
1524:math/0605667
1514:
1510:
1500:
1491:math/0303109
1479:
1454:math/9404236
1444:
1438:
1432:
1418:
1404:
1392:. Retrieved
1385:
1362:
1334:. Retrieved
1324:
1310:
1292:See p. 3 in
1288:
1277:. Retrieved
1267:
1243:
1237:
1223:Gabai, David
1067:
1052:
1036:
1029:
1022:
1016:Ann. of Math
1011:
997:
988:
969:
958:
942:
933:
925:Fields Medal
922:
911:
887:
872:
863:
848:Please help
836:
795:generalized
790:
774:
764:
762:
751:
744:
704:
681:Robert Riley
662:
647:
638:
627:Please help
622:verification
619:
589:
553:three-sphere
527:
514:
510:adding to it
505:
470:Oded Schramm
431:
428:
417:
394:
383:
373:
362:intuitionist
355:
337:
313:
305:Fields Medal
292:
291:
273:Oded Schramm
214:
175:Institutions
158:
126:Fields Medal
72:(2012-08-21)
2834:2012 deaths
2829:1946 births
2794:André Neves
2784:Daniel Wise
2774:Paul Seidel
2742:David Gabai
2660:Barry Mazur
2534:2022
2507:2018
2480:2014
2453:2010
2426:2006
2409:2002
2382:1998
2355:1994
2328:1990
2306:1986
2284:1982
2257:1978
2240:1974
2213:1970
2186:1966
2169:1962
2152:1958
2135:1954
2118:1950
2101:1936
1858:Reviews of
1794:"YEAR 1990"
929:3-manifolds
916:shared the
797:Lipman Bers
770:3-manifolds
731:irreducible
669:3-manifolds
546:codimension
462:Yair Minsky
450:Benson Farb
442:David Gabai
358:New College
347: Martt
309:3-manifolds
265:Yair Minsky
249:David Gabai
245:Benson Farb
169:Mathematics
2823:Categories
2644:Raoul Bott
2497:Mirzakhani
2394:Kontsevich
1868:0764.20017
1806:30 January
1755:2008-06-26
1336:2013-09-06
1301:1912.03115
1279:2023-01-11
1182:References
939:Book Prize
902:Ricci flow
866:March 2022
711:decomposed
696:hyperbolic
692:complement
641:March 2022
572:cohomology
489:Foliations
466:Igor Rivin
351:strabismus
269:Igor Rivin
146:Doob Prize
51:1946-10-30
2722:Gang Tian
2551:Viazovska
2524:Venkatesh
2416:Voevodsky
2411:Lafforgue
2384:Borcherds
2308:Donaldson
2264:Fefferman
2171:Hörmander
1876:Bull. AMS
1716:18 August
1669:March 24,
1651:1364-0380
1589:0001-5962
1543:1364-0380
1394:March 25,
1332:. Ias.edu
837:does not
749:theorem.
530:foliation
517:June 2008
376:in 1972.
78:Rochester
2808:Song Sun
2780:Ian Agol
2573:Category
2487:Bhargava
2433:Perelman
2428:Okounkov
2399:McMullen
2372:Zelmanov
2357:Bourgain
2330:Drinfeld
2318:Freedman
2313:Faltings
2291:Thurston
2269:Margulis
2242:Bombieri
2230:Thompson
2220:Hironaka
2120:Schwartz
1884:Bull LMS
1777:Archived
1663:Archived
1659:14463721
1597:10138438
1256:Archived
1229:(2015).
1083:See also
976:melanoma
890:orbifold
484:Research
409:UC Davis
401:Berkeley
116:Orbifold
2546:Maynard
2519:Scholze
2514:Figalli
2470:Villani
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