Geodesically Tracking Quasi-geodesic Paths for Coxeter Groups

Details Geodesically Tracking Quasi-geodesic Paths for Coxeter Groups Geodesically Tracking Quasi-geodesic Paths for Coxeter Groups

2011-12-15

arxiv.org/abs/1112.3397v1

Mathematics

Group Theory

15 pages, 5 figures

Scientific paper

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.

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