All Questions
5
questions
4
votes
0
answers
65
views
Is there an algorithm to check that a subgroup of a CAT$(0)$ group is *not* quasiconvex?
Let $G$ be a finitely generated CAT$(0)$ group and $H$ a subgroup. If $H$ is quasiconvex then it is finitely generated, so we can immediately conclude that any non-finitely generated subgroup of $G$ ...
- 2,382
3
votes
1
answer
72
views
Davis Regular Tessellations of Spheres and Straight Line Coxeter Groups
In Davis' "Geometry and Topology of Coxeter Groups", section B.3, in particular Theorem B.3.1, there is a proof that every finite "straight line" Coxeter group is associated to a ...
- 168
3
votes
1
answer
84
views
The Bruhat Orders of (finite irreducible) Coxeter Groups as Polytopes
The Strong Bruhat Order of a finite irreducible Coxeter Group satisfies all the axioms of being an abstract polytope. It's also a remarkably nice fact that the Weak Bruhat Order of the Symmetric Group ...
- 317
2
votes
1
answer
97
views
Embedding of the 1-skeleton of a Coxeter group into its Davis complex
Let $(W,S)$ be a Coxeter system and let $\Sigma$ be the corresponding Davis complex. It is well-known that the Davis complex may be equipped with a piecewise Euclidean metric so that it is a proper, ...
- 937
4
votes
2
answers
584
views
When is a right-angled Coxeter group one-ended?
Let $\Gamma$ be a simplicial graph (ie. without multiple edes nor loops). We define the associated right-angled Artin group $A(\Gamma)$ by the presentation
$$\langle v \in V(\Gamma) \mid [u,v]=1 \ \...
- 33.3k