Coxeter groups and random groups
Group Theory
2015-04-07 v2 Geometric Topology
Abstract
For every dimension d, there is an infinite family of convex co-compact reflection groups of isometries of hyperbolic d-space --- the superideal (simplicial and cubical) reflection groups --- with the property that a random group at any density less than a half (or in the few relators model) contains quasiconvex subgroups commensurable with some member of the family, with overwhelming probability.
Cite
@article{arxiv.1411.1506,
title = {Coxeter groups and random groups},
author = {Danny Calegari},
journal= {arXiv preprint arXiv:1411.1506},
year = {2015}
}
Comments
18 pages, 14 figures; version 2 incorporates referee's corrections