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boundary have at most "half" of all possible boundary slopes resulting from essential surfaces. In the case of one torus boundary, one can conclude that the number of slopes given by essential surfaces is finite.
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3-manifolds and extended the techniques and line of investigation started in
Thurston's Princeton lecture notes. Hatcher also showed that irreducible,
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in 3-manifolds. He invented the notion of "end-incompressibility" and several of his students, such as Mark
Brittenham, Charles Delman, and
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postdoc for a year, then a lecturer for another year, and then
Assistant Professor from 1973 to 1979. He was also a member of the
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and
Hatcher classified all the incompressible surfaces in punctured-torus bundles over the circle.
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Perhaps among his most recognized results in 3-manifolds concern the classification of
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Hatcher and
Thurston exhibited an algorithm to produce a presentation of the
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A presentation for the mapping class group of a closed orientable surface,
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as an assistant professor in 1977. From 1983 he has been a professor at
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947:"Annual Report for the Fiscal Year July 1, 1979–June 30, 1980"
839:{\displaystyle \mathrm {Diff} (S^{3})\simeq {\mathrm {O} }(4)}
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from the article and its talk page, especially if potentially
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Hatcher has made contributions to the so-called theory of
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and
Hatcher classified the incompressible surfaces in
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Incompressible surfaces in 2-bridge knot complements,
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Incompressible surfaces in punctured-torus bundles,
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734:On the boundary curves of incompressible surfaces,
627:in certain 3-manifolds and their boundary slopes.
642:. As corollaries, this gave more examples of non-
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1101:Institute for Advanced Study visiting scholars
1106:University of California, Los Angeles faculty
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556:in 1975–76 and 1979–80. Hatcher moved to the
521:in 1966, he went for his graduate studies to
53:Learn how and when to remove these messages
902:"Spectral Sequences in Algebraic Topology"
577:International Congresses of Mathematicians
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97:about living persons that is unsourced or
299:Learn how and when to remove this message
281:Learn how and when to remove this message
168:Learn how and when to remove this message
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701:and moves that relate any two systems.
697:. Their work relied on the notion of a
537:, was written under the supervision of
493:(born October 23, 1944) is an American
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558:University of California, Los Angeles
422:University of California, Los Angeles
1086:21st-century American mathematicians
1081:20th-century American mathematicians
591:, both in high dimensions, relating
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991:"Allen Hatcher, Professor Emeritus"
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1011:. International Mathematical Union
1009:"ICM Plenary and Invited Speakers"
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14:
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780:A proof of the Smale conjecture,
442:Obstruction for Pseudo-Isotopies
34:This article has multiple issues.
535:Obstruction for Pseudo-Isotopies
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23:
911:"Basic Topology of 3-Manifolds"
42:or discuss these issues on the
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737:Pacific Journal of Mathematics
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1034:"Hatcher's personal homepage"
993:. Department of Mathematics,
979:Mathematics Genealogy Project
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893:"Vector Bundles and K-Theory"
753:Topology and its Applications
211:secondary or tertiary sources
1096:Princeton University faculty
954:Institute for Advanced Study
554:Institute for Advanced Study
544:Afterwards, Hatcher went to
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217:, especially if potentially
195:biography of a living person
75:biography of a living person
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1066:Mathematicians from Indiana
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215:must be removed immediately
102:must be removed immediately
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583:Mathematical contributions
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866:Hatcher, Allen (2002).
855:(1983), no. 3, 553–607.
775:(1985), no. 2, 225–246.
758:(1982), no. 3, 263–282.
742:(1982), no. 2, 373–377.
729:(1980), no. 3, 221–237.
625:incompressible surfaces
571:In 1978 Hatcher was an
1071:Oberlin College alumni
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607:, such as proving the
513:. After obtaining his
209:Please help by adding
89:Please help by adding
16:American mathematician
920:"Topology of Numbers"
849:Annals of Mathematics
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705:Selected publications
668:essential laminations
529:in 1971. His thesis,
1091:American topologists
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656:boundary-irreducible
546:Princeton University
505:Hatcher was born in
491:Allen Edward Hatcher
418:Princeton University
341:Allen Edward Hatcher
95:Contentious material
748:and Allen Hatcher,
684:mapping class group
523:Stanford University
391:Stanford University
198:relies too much on
995:Cornell University
956:. 1980. p. 41
869:Algebraic topology
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761:Allen Hatcher and
715:Allen Hatcher and
597:algebraic K-theory
589:geometric topology
566:professor emeritus
562:Cornell University
548:, where he was an
426:Cornell University
658:3-manifolds with
587:He has worked in
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398:Scientific career
327:Allen Hatcher at
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573:invited speaker
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593:pseudoisotopy
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579:in Helsinki.
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1013:. Retrieved
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84:verification
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36:Please help
33:
1051:1944 births
652:irreducible
640:complements
619:3-manifolds
605:3-manifolds
408:Mathematics
373:Nationality
221:or harmful.
1045:Categories
1015:2024-07-03
960:January 3,
928:References
699:cut system
692:orientable
495:topologist
347:1944-10-23
241:newspapers
200:references
128:newspapers
39:improve it
818:≃
501:Biography
271:July 2012
158:July 2012
80:citations
45:talk page
724:Topology
678:Surfaces
613:3-sphere
611:for the
601:surfaces
377:American
329:Berkeley
219:libelous
106:libelous
977:at the
695:surface
575:at the
511:Indiana
362:Indiana
331:in 1980
255:scholar
142:scholar
880:
710:Papers
688:closed
646:, non-
446:(1971)
444:
433:Thesis
404:Fields
257:
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137:
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115:
950:(PDF)
860:Books
686:of a
660:toral
644:Haken
527:Ph.D.
517:from
262:JSTOR
248:books
193:This
149:JSTOR
135:books
73:This
962:2021
878:ISBN
851:(2)
603:and
337:Born
234:news
121:news
82:for
853:117
595:to
550:NSF
531:A K
515:B.S
438:A K
202:to
1047::
952:.
936:^
876:.
773:79
765:,
756:13
740:99
727:19
719:,
690:,
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615:.
568:.
541:.
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997:.
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831:4
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51:(
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