On the geometric and topological rigidity of hyperbolic 3-manifolds

David Gabai

doi:10.1090/S0273-0979-1994-00523-3

On the geometric and topological rigidity of hyperbolic 3-manifolds

David Gabai

Research output: Contribution to journal › Comment/debate › peer-review

3 Scopus citations

Abstract

A homotopy equivalence between a hyperbolic 3-manifold and a closed irreducible 3-manifold is homotopic to a homeomorphsim provided the hyperbolic manifold satisfies a purely geometric condition. There are no known examples of hyperbolic 3-manifolds which do not satisfy this condition.

Original language	English (US)
Pages (from-to)	228-232
Number of pages	5
Journal	Bulletin of the American Mathematical Society
Volume	31
Issue number	2
DOIs	https://doi.org/10.1090/S0273-0979-1994-00523-3
State	Published - Oct 1994
Externally published	Yes

All Science Journal Classification (ASJC) codes

General Mathematics
Applied Mathematics

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10.1090/S0273-0979-1994-00523-3

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abstract = "A homotopy equivalence between a hyperbolic 3-manifold and a closed irreducible 3-manifold is homotopic to a homeomorphsim provided the hyperbolic manifold satisfies a purely geometric condition. There are no known examples of hyperbolic 3-manifolds which do not satisfy this condition.",

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year = "1994",

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AU - Gabai, David

PY - 1994/10

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N2 - A homotopy equivalence between a hyperbolic 3-manifold and a closed irreducible 3-manifold is homotopic to a homeomorphsim provided the hyperbolic manifold satisfies a purely geometric condition. There are no known examples of hyperbolic 3-manifolds which do not satisfy this condition.

AB - A homotopy equivalence between a hyperbolic 3-manifold and a closed irreducible 3-manifold is homotopic to a homeomorphsim provided the hyperbolic manifold satisfies a purely geometric condition. There are no known examples of hyperbolic 3-manifolds which do not satisfy this condition.

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U2 - 10.1090/S0273-0979-1994-00523-3

DO - 10.1090/S0273-0979-1994-00523-3

M3 - Comment/debate

AN - SCOPUS:84967787227

SN - 0273-0979

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EP - 232

JO - Bulletin of the American Mathematical Society

JF - Bulletin of the American Mathematical Society

IS - 2

ER -

On the geometric and topological rigidity of hyperbolic 3-manifolds

Abstract

All Science Journal Classification (ASJC) codes

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