Topology and Geometric Group Theory Seminar
A group G is hyperbolic relative to a collection of subgroups P if G acts properly by isometries on a Gromov hyperbolic space X with a cusp uniform action. P is the collection of maximal parabolic subgroups of this action. The Bowditch boundary of (G,P) is defined to be the boundary of the space X. If the subgroups in P are not properly relatively hyperbolic, then the homeomorphism type of the Bowditch boundary is known to be a quasi-isometry invariant of G. In this talk we will discuss ways in which the Bowditch boundary can be used to distinguish between quasi-isometry classes of certain right-angled Coxeter groups. This is joint work with Hoang Nguyen (UW-Milwaukee) and Hung Cong Tran (UGA).