RTG Seminar on Geometry, Dynamics and Topology

Last week we studied Auslander's 'conjecture' that the fundamental group of a complete closed affine manifold is virtually solvable, and the related question by Milnor, whether this remains true without requiring the manifold to be closed. This week I will explain Margulis' construction of (noncompact) examples in dimension 3 with free fundamental group, answering Milnor's question in the negative. We will also see how Goldman-Margulis combined the key new tool for this construction, the Margulis invariant, with Teichmueller theory to give a new proof of a theorem of Mess: Any counterexample to Milnor's question has to have free fundamental group. Speaker(s): Wouter Van Limbeek (University of Michigan)