All Questions
7 questions with no upvoted or accepted answers
10
votes
0
answers
458
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is a group $G$, that admits finite $k(G, 1)$ and has no Baumslag-Solitar subgroups, necessarily hyperbolic?
This is the first question asked in Bestvina's article "Questions in Geometric Group Theory". Does anyone know if there has been any progress made on this problem? Is the question answered if $G$ is ...
- 101
5
votes
0
answers
140
views
Reference request: Name or use of this group of diffeomorphisms of the disc
Let $k \in \{0,\infty\}$, $G\subseteq \operatorname{Diff}^k(D^n)$ be the set of diffeomorphisms $\phi:D^n\to D^n$ of the closed $n$-disc $D^n$ (with its boundary) satisfying the following:
$
\phi(S_r^...
- 5,405
4
votes
0
answers
453
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Problem 1.8 from Kirby's list
Context
I looked through a book called "Problems in Low-Dimensional Topology", where Rob Kirby lists a set of problems. He provides a list of problems, states their conjectures, and ...
3
votes
0
answers
115
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Finite homology of a homogeneous space
Let $\Gamma$ be a cocompact lattice in $\operatorname{SL}(2,\mathbb R)$ and $X=\operatorname{SL}(2,\mathbb R)/\Gamma$ be the underlying homogeneous space. Can the homology group $H_1(X,\mathbb Z)$ be ...
3
votes
0
answers
393
views
What about a Cayley n-complex for n>2?
Let $G$ be a finitely presented group. The Cayley graph of the finite generating set is a $1$-complex where the $0$-cells are the elements of $G$ and the $1$-cells are given by the generators (...
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
1
vote
0
answers
113
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Question on models for $EG$ for a $G$-CW complex
I am having trouble finding information on a definition in P. Hanham's PhD thesis paper. recall that given a discrete group $G$ a $G$-CW-complex $X$ is a CW-complex equipped with a topological $G$ ...
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