Geodesically Tracking Quasi-geodesic Paths for Coxeter Groups
Group Theory
2014-02-26 v1 Geometric Topology
Abstract
The main theorem of this paper classifies the quasi-geodesics in a Coxeter group that are tracked by geodesics. As corollaries, we show that if a Coxeter group acts geometrically on a CAT(0) space X then CAT(0) rays (and lines) are tracked by Cayley graph geodesics, all special subgroups of the Coxeter group are quasi-convex in X, and in Cayley graphs for Coxeter groups, elements of infinite order are tracked by geodesics.
Cite
@article{arxiv.1112.3397,
title = {Geodesically Tracking Quasi-geodesic Paths for Coxeter Groups},
author = {Michael L. Mihalik and Steven Tschantz},
journal= {arXiv preprint arXiv:1112.3397},
year = {2014}
}
Comments
15 pages, 5 figures