Seminar

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A discrete surface subgroup of GL(4,R) acts on 3-dimensional projective space, and the groups that act nicely on a properly convex domain form a stable class. We are interested in a) what kinds of topological and geometrical invariants classify these objects and b) how do they degenerate? These are both questions that have been answered for Kleinian surface subgroups of SO(3,1)<GL(4,R).

In this talk, I will focus on a special class of subgroups that fix a point in RP^3 and identify the degenerations of convex cocompact surface subgroups within this class.  The goal will be to describe a beautiful connection between the limit sets of such “degenerate” surface groups and the geometry of the stable norm on homology with respect to a certain asymmetric metric on the surface introduced by Danciger—Stecker.  There is, in particular, an oriented geodesic lamination of maximal stretch whose positive endpoints are all crushed to the same point in the limit set.  

My hope is that this talk, based on joint work with Marit Bobb, will be interesting and accessible to members of both programs.