User HJRW

47 votes

Most interesting mathematics mistake?

answered Dec 15, 2009 at 19:14

43 votes

What are some of the big open problems in 3-manifold theory?

answered Aug 22, 2010 at 22:07

39 votes

finite generated group realized as fundamental group of manifolds

answered Feb 16, 2010 at 3:12

37 votes

What are your favorite instructional counterexamples?

answered Mar 2, 2010 at 19:00

29 votes

Can a group be a universal Turing machine?

answered Feb 14, 2012 at 10:01

27 votes

Accepted

Mapping from a finite index subgroup onto the whole group

answered Mar 2, 2012 at 13:19

27 votes

Accepted

Does injectivity of $\pi_1(\partial U) \to \pi_1(M)$ imply injectivity of $\pi_1(U) \to \pi_1(M)$?

answered Oct 18, 2019 at 9:35

25 votes

Accepted

Primes occurring as orders of elements of a finitely presented group

answered Feb 8, 2013 at 13:03

25 votes

Accepted

Fundamental group of 3-manifold with boundary

answered Nov 19, 2009 at 18:04

24 votes

Accepted

Modern references on hyperbolic groups

answered Sep 4, 2018 at 14:20

21 votes

Accepted

Does the injection $\text{Aut}(F_n) \hookrightarrow \text{Aut}(F_{n+1})$ split?

answered May 19, 2016 at 20:34

21 votes

When is a extension of $\mathbb{Z}$ by a free group a CAT(0) group?

answered Feb 1, 2011 at 15:46

21 votes

Fundamental groups of closed hyperbolic 3-manifolds are freely indecomposable

answered Mar 9, 2011 at 4:33

20 votes

〈x,y : x^p = y^p = (xy)^p = 1〉

answered Apr 24, 2010 at 23:18

19 votes

Accepted

What are the implications of the simple loop conjecture?

answered Nov 30, 2015 at 21:27

19 votes

Accepted

A result of Schützenberger on commutators and powers in free groups

answered Dec 8, 2016 at 16:28

19 votes

Residual finiteness: why do we care?

answered Feb 28, 2015 at 4:30

19 votes

Acyclic group and finite CW-complex

answered Feb 5, 2020 at 21:57

18 votes

Examples of locally hyperbolic groups

answered Jul 4, 2022 at 9:23

18 votes

Accepted

Is there a finitely presented group with infinite homology over $\mathbb{Q}$?

answered Aug 7, 2014 at 5:09

17 votes

Accepted

Is the diagonal of finitely presented groups computable?

answered Apr 22, 2021 at 8:47

17 votes

How helpful is non-standard analysis?

answered Feb 25, 2010 at 0:38

17 votes

When is a finitely generated group finitely presented?

answered Feb 10, 2011 at 3:33

17 votes

A single paper everyone should read?

answered Nov 8, 2009 at 5:18

17 votes

Applications of the notion of of Gromov-Hausdorff distance

answered Feb 27, 2011 at 13:15

16 votes

Accepted

Conjugacy classes of the mapping class group

answered Jan 1, 2020 at 12:16

16 votes

Examples of finitely presented subgroups of $\operatorname{GL}(n,\mathbb{Z})$ with unsolvable decision problems

answered Jun 3 at 15:01

15 votes

Accepted

Number of subgroups of a given index of a free group

answered Dec 2, 2013 at 5:46

15 votes

Understanding groups that are not linear

answered Oct 21, 2012 at 18:38

15 votes

Accepted

Judging whether a finitely presented group is a 3-manifold group?

answered Oct 22, 2012 at 9:38

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301 Answers

Most interesting mathematics mistake?

What are some of the big open problems in 3-manifold theory?

finite generated group realized as fundamental group of manifolds

What are your favorite instructional counterexamples?

Can a group be a universal Turing machine?

Mapping from a finite index subgroup onto the whole group

Does injectivity of $\pi_1(\partial U) \to \pi_1(M)$ imply injectivity of $\pi_1(U) \to \pi_1(M)$?

Primes occurring as orders of elements of a finitely presented group

Fundamental group of 3-manifold with boundary

Modern references on hyperbolic groups

Does the injection $\text{Aut}(F_n) \hookrightarrow \text{Aut}(F_{n+1})$ split?

When is a extension of $\mathbb{Z}$ by a free group a CAT(0) group?

Fundamental groups of closed hyperbolic 3-manifolds are freely indecomposable

〈x,y : x^p = y^p = (xy)^p = 1〉

What are the implications of the simple loop conjecture?

A result of Schützenberger on commutators and powers in free groups

Residual finiteness: why do we care?

Acyclic group and finite CW-complex

Examples of locally hyperbolic groups

Is there a finitely presented group with infinite homology over $\mathbb{Q}$?

Is the diagonal of finitely presented groups computable?

How helpful is non-standard analysis?

When is a finitely generated group finitely presented?

A single paper everyone should read?

Applications of the notion of of Gromov-Hausdorff distance

Conjugacy classes of the mapping class group

Examples of finitely presented subgroups of $\operatorname{GL}(n,\mathbb{Z})$ with unsolvable decision problems

Number of subgroups of a given index of a free group

Understanding groups that are not linear

Judging whether a finitely presented group is a 3-manifold group?