Topology Seminar (Introductory Talk): Expanding maps on manifolds

Seminar | February 15 | 2:10-3 p.m. | 736 Evans Hall

 Wouter van Limbeek, University of Michigan

 Department of Mathematics

Suppose M is a manifold that covers itself nontrivially. What can we say about M? In general this is a difficult question. In this talk we will consider this problem with the further dynamical assumption that the map is expanding (with respect to some auxiliary metric). These maps have been completely classified (by combined work of Shub, Franks, and Gromov): Any closed manifold that admits an expanding map is infranil, and the map is conjugate to an endomorphism of the corresponding nilpotent Lie group.