The geodesic flow of a nonpositively curved graph manifold

Abstract

We study discrete, cocompact, isometric actions of groups on Hadamard spaces, and the induced actions on ideal boundaries. For a class of groups generalizing fundamental groups of three-dimensional graph manifolds, we find a set of invariants for the action which determine the boundary action up to equivariant homeomorphism. This work was inspired by (and answers) a question of Gromov from "Asymptotic invariants of infinite groups."