Groups and Dynamics Seminar

We are interested in surface subgroups of GL(4,R) via their actions on 3-dimensional projective space. Many such surface subgroups are (projective)-Anosov and preserve a properly convex subset of projective space on which the action is proper.  I will focus on a special class that fix a point in RP^3. In this setting, it is possible to identify the representations that can be approached by Anosov representations, but which fail the Anosov condition. The goal of the talk will be to describe a beautiful connection between the limit sets of such “degenerate” surface group actions and the geometry of the “stable norm” or homology with respect to an asymmetric metric on the surface introduced by Danciger-Stecker. There is, in particular, an oriented geodesic lamination of maximal stretch whose endpoints are all crushed to the same point in the limit set. This is joint work with Marit Bobb.