Marit Bobb
MPI Leipzig
Title
Convex cocompact surface group representations and affine laminations
Abstract
Convex cocompact representations of surface groups acting on H^3 are central to our understanding of hyperbolic 3-manifolds. Meanwhile, convex cocompact surface groups acting on anti-de Sitter space (AdS^3) give a proof of Thurston's earthquake theorem (by Mess). These two beautiful and complementary stories are unified when considering convex cocompact actions of surface groups on the 3-dimensional projective space, which is considerably harder to understand in full.
In joint work with James Farre, we make a first step toward a more general theory of convex cocompactness in projective space by exploring coaffine representations (to be defined in the course of the talk). We will show that while measured laminations parametrize this space, the measures manifest with nontrivial holonomy: they are affine measured laminations