Appears in collection : Homogeneous Dynamics and Geometry in Higher-Rank Lie Groups

In this talk, I will discuss transverse groups (also called antipodal regular groups), a discrete group class containing the Anosov and relatively Anosov ones. I will describe a metric and flow space such a group acts on, which are analogous to the Cayley graph and the geodesic flow space of a word hyperbolic group. Then I will discuss how to use these spaces to prove new results. This represents joint work with Richard Canary and Tengren Zhang.