Divergence of CAT(0) Cube Complexes and Coxeter Groups
arXiv:1611.04378 · doi:10.2140/agt.2018.18.1633
Abstract
We provide geometric conditions on a pair of hyperplanes of a CAT(0) cube complex that imply divergence bounds for the cube complex. As an application, we classify all right-angled Coxeter groups with quadratic divergence and show right-angled Coxeter groups cannot exhibit a divergence function between quadratic and cubic. This generalizes a theorem of Dani-Thomas that addressed the class of 2-dimensional right-angled Coxeter groups. As another application, we provide an inductive graph theoretic criteria on a right-angled Coxeter group's defining graph which allows us to recognize arbitrary integer degree polynomial divergence for many infinite classes of right-angled Coxeter groups. We also provide similar divergence results for some classes of Coxeter groups which are not right-angled.
Final prepublished version. This article now appears in Algebraic & Geometric Topology
References in corpus (1)
Cited by in corpus (6)
- A remark on thickness of free-by-cyclic groups
- Sublinearly Morse Geodesics in CAT(0) Spaces: Lower Divergence and Hyperplane Characterization
- On the coarse geometry of certain right-angled Coxeter groups
- Divergence of finitely presented subgroups of CAT(0) groups
- Divergence, thickness and hypergraph index for general Coxeter groups
- Detecting a subclass of torsion-generated groups