User Allen Hatcher

19 votes

Closed manifold with non-vanishing homotopy groups and vanishing homology groups

answered Apr 23, 2019 at 21:03

18 votes

Topological structure of SO(n) as a product

answered Oct 8, 2015 at 20:16

18 votes

Accepted

Poincaré Duality for non-compact manifolds without Zorn's Lemma

answered May 13, 2016 at 15:29

17 votes

Accepted

Easiest example where pseudo-isotopy fails to be the same as isotopy?

answered Sep 9, 2016 at 2:52

17 votes

Spaces with both "simple homology" and "simple homotopy" at the same time

answered Jun 29, 2010 at 12:45

16 votes

Killing the torsion in homotopy

answered Jan 5, 2010 at 3:32

16 votes

Mapping Class Group (MCG) of connected sum of 3-torus and $S^2\times S^1$

answered Jul 29, 2016 at 13:35

16 votes

Topological $n$-manifolds have the homotopy type of $n$-dimensional CW-complexes

answered Apr 4, 2015 at 13:03

16 votes

Accepted

what is this simple topological space?

answered Jan 24 at 1:50

15 votes

Accepted

Homotopy type of set of self homotopy-equivalences of a surface

answered Mar 19, 2010 at 3:51

15 votes

Accepted

Is geometric realization of the total singular complex of a space homotopy equivalent to the space?

answered May 22, 2010 at 1:41

15 votes

Calculating cup products using cellular cohomology

answered Oct 23, 2010 at 15:44

15 votes

Satellite knot example

answered Apr 28, 2013 at 0:50

15 votes

Accepted

Mapping class groups of small Seifert-fibred 3-manifolds

answered Nov 17, 2013 at 3:50

14 votes

Accepted

Seifert fiberable manifolds with several Seifert fiberings

answered Feb 16, 2014 at 22:45

14 votes

Accepted

How to prove the isotopy relative to a point exist?

answered Dec 24, 2012 at 0:48

14 votes

Deeper meanings of barycentric subdivision

answered Jul 8, 2010 at 15:26

14 votes

Accepted

Can H-space multiplication always be straightened so that mult.-by-id. is the identity on the nose?

answered Apr 19, 2010 at 10:15

14 votes

Periodic mapping classes of the genus two orientable surface

answered Dec 4, 2009 at 5:50

14 votes

Accepted

Geometric intuition behind this chain homotopy

answered Nov 11, 2019 at 0:36

14 votes

Accepted

Mapping class group of certain 3-manifolds

answered Jun 8, 2017 at 4:04

14 votes

Accepted

Homotopically trivial vs isotopically trivial diffeomorphisms

answered Aug 28, 2016 at 1:26

13 votes

Accepted

How can I endow a "locally product" CW structure on a vector bundle over a CW complex?

answered Jun 19, 2017 at 2:34

13 votes

Accepted

Proof of the stable homeomorphism conjecture

answered Apr 29, 2017 at 11:11

13 votes

Accepted

Where was it first shown that every homotopy self-equivalence of $S^1\times S^2$ is homotopic to a homeomorphism?

answered Feb 16, 2021 at 5:12

13 votes

Accepted

Two solid N_3 glued by its boundary

answered Dec 6, 2009 at 16:15

13 votes

Accepted

About the proof of Wajnryb's finite presentation of Mod(S)

answered Jun 5, 2010 at 9:57

13 votes

Accepted

Textbook for undergraduate course in geometry

answered Nov 1, 2012 at 14:57

12 votes

Accepted

Does there exist a Haken manifold where all its incompressible surfaces are non-separating?

answered Nov 7, 2017 at 19:56

11 votes

Diffeomorphism group of the projective plane

answered Feb 17, 2022 at 13:13

Stack Exchange Network

114 Answers

Closed manifold with non-vanishing homotopy groups and vanishing homology groups

Topological structure of SO(n) as a product

Poincaré Duality for non-compact manifolds without Zorn's Lemma

Easiest example where pseudo-isotopy fails to be the same as isotopy?

Spaces with both "simple homology" and "simple homotopy" at the same time

Killing the torsion in homotopy

Mapping Class Group (MCG) of connected sum of 3-torus and $S^2\times S^1$

Topological $n$-manifolds have the homotopy type of $n$-dimensional CW-complexes

what is this simple topological space?

Homotopy type of set of self homotopy-equivalences of a surface

Is geometric realization of the total singular complex of a space homotopy equivalent to the space?

Calculating cup products using cellular cohomology

Satellite knot example

Mapping class groups of small Seifert-fibred 3-manifolds

Seifert fiberable manifolds with several Seifert fiberings

How to prove the isotopy relative to a point exist?

Deeper meanings of barycentric subdivision

Can H-space multiplication always be straightened so that mult.-by-id. is the identity on the nose?

Periodic mapping classes of the genus two orientable surface

Geometric intuition behind this chain homotopy

Mapping class group of certain 3-manifolds

Homotopically trivial vs isotopically trivial diffeomorphisms

How can I endow a "locally product" CW structure on a vector bundle over a CW complex?

Proof of the stable homeomorphism conjecture

Where was it first shown that every homotopy self-equivalence of $S^1\times S^2$ is homotopic to a homeomorphism?

Two solid N_3 glued by its boundary

About the proof of Wajnryb's finite presentation of Mod(S)

Textbook for undergraduate course in geometry

Does there exist a Haken manifold where all its incompressible surfaces are non-separating?

Diffeomorphism group of the projective plane