Seminar

This talk describes joint work with Suhyoung Choi.  A Margulis spacetime is a 3-dimensional affine space form M whose fundamental group is a finitely generated nonabelian free group. Equivalently, M is a quotient of 3-dimensional Minkowski space by a proper affine deformation of a Fuchsian subgroup G of SO(2,1). When G is a convex cocompact, we show M is homeomorphic to the interior of a compact manifold-with-boundary with a 3-dimensional real-projective structure. This implies that M is an open solid handlebody. The methods involve an orbit equivalence between the geodesic flow of the hyperbolic surface defined by G and the spacelike-Lorentzian geodesic flow on the flat 3-manifold M  (joint work with Francois Labourie and Gregory Margulis).  

Using quite different methods, this was independently proved by Jeffrey Danciger, François Guéritaud and Fanny Kassel.