Infinitely many hyperbolic Coxeter groups through dimension 19
Group Theory
2009-03-17 v2 Geometric Topology
Abstract
We prove the following: there are infinitely many finite-covolume (resp. cocompact) Coxeter groups acting on hyperbolic space H^n for every n < 20 (resp. n < 7). When n=7 or 8, they may be taken to be nonarithmetic. Furthermore, for 1 < n < 20, with the possible exceptions n=16 and 17, the number of essentially distinct Coxeter groups in H^n with noncompact fundamental domain of volume less than or equal to V grows at least exponentially with respect to V. The same result holds for cocompact groups for n < 7. The technique is a doubling trick and variations on it; getting the most out of the method requires some work with the Leech lattice.
Cite
@article{arxiv.0903.0138,
title = {Infinitely many hyperbolic Coxeter groups through dimension 19},
author = {Daniel Allcock},
journal= {arXiv preprint arXiv:0903.0138},
year = {2009}
}
Comments
This is the version published by Geometry & Topology on 11 July 2006 (V2: typesetting correction)