All Questions
7 questions
5
votes
1
answer
512
views
What are the cohomological dimensions of ${\rm Aut}(F_n)$, ${\rm Out}(F_n)$, ${\rm SL}_n(\mathbb{Z})$ over the rationals ℚ and integers ℤ?
$\DeclareMathOperator\Aut{Aut}\DeclareMathOperator\Out{Out}\DeclareMathOperator{\cd}{cd}\DeclareMathOperator\SL{SL}$For a group $G$, the cohomological dimension of $G$ over the ring $R$, denoted by $\...
- 331
3
votes
0
answers
128
views
Salvetti complexes and cohomology of affine completion of Artin groups $E_6$ and $E_7$
After the solution of the Brieskorn-Arnold Pham conjecture on the asphericity of a space for affine Artin groups by Paolini and Salvetti MR4243019 (arXiv), I would like to know if there are ...
- 2,630
13
votes
1
answer
289
views
Powers of the Euler class, torsion free subgroup of Homeo($S^1$)
For any subgroup $G$ of $\text{Homeo}(S^1)$, we have the Euler class $\chi$ in the group cohomology $H^2(G;\mathbb{Z})$. One can think of this class as the pullback of the generator of $H^2(\mathrm{B}\...
- 1,003
24
votes
1
answer
968
views
Groups whose finite index subgroups of fixed index are isomorphic
I am interested in finitely generated groups $G$ that are residually finite and have the following property: For each $d \geq 1$, $G$ has subgroups of finite index $d$, and all such subgroups are ...
- 11.9k
1
vote
0
answers
278
views
Homology of spherical braid groups
By the spherical braid group, I mean the fundamental group of the configuration space of distinct unordered points in $S^2$. I am wondering what is known about the group homology of the spherical ...
- 116
15
votes
1
answer
640
views
Torsion-free group that is not of type F but is virtually of type F
Recall that a group $G$ is of type F if there exists a compact $K(G,1)$.
There are many examples of groups which are not of type F but which are virtually of type F, that is, they have finite-index ...
- 153
10
votes
1
answer
580
views
Nonhyperbolic groups that contain no free abelian groups or Baumslag-Solitar groups
I've heard it conjectured that a finitely presentable group $G$ is hyperbolic if it satisfies the following two conditions.
$G$ contains no subgroup isomorphic to a Baumslag-Solitar group $BS(n,m)$ (...
- 103