Geodesically Tracking Quasi-geodesic Paths for Coxeter Groups
arXiv:1112.3397 · doi:10.1112/blms/bds125
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.
15 pages, 5 figures