Geodesically Tracking Quasi-Geodesic Paths for Coxeter Groups
Michael Mihalik, Vanderbilt University
Location: Stevenson 1310
If (W,S) is a finitely generated Coxeter system we classify the quasi-geodesic paths (rays or lines) in the corresponding Cayley graph that are tracked by geodesics. The main corollary is that if W acts geometrically on a CAT(0) space X, then geometric geodesics in X are tracked by Cayley geodesics in X. This allows one to effectively transfer the group theory and combinatorics of (W,S) to help analyze the (local and asymptotic) geometry of X.