11/09: Andrew Zimmer
Convex co-compact representations of 3-manifold groups
Abstract: A representation of a finitely generated group into the projective linear group is called convex co-compact if it has finite kernel and its image acts convex co-compactly on a properly convex domain in real projective space. In this talk I will discuss the case of 3-manifold groups and prove that the fundamental group of a closed irreducible orientable 3-manifold can admit such a representation only when the manifold is geometric (with Euclidean, Hyperbolic, or Euclidean × Hyperbolic geometry) or when every component in the geometric decomposition is hyperbolic. This extends a result of Benoist about convex real projective structures on closed 3-manifolds. In each case, I will also describe what these representations look like. This is joint work with Mitul Islam (a graduate student at the University of Michigan).