Date/Time Date(s) - 22/11/202412:00 pm - 1:00 pm
Location: Hamilton Hall, Room 207
Speaker: Danny Ruberman (Brandeis University)
Title: Exotic aspherical 4-manifolds
Abstract: An aspherical space is one with vanishing higher homotopy groups; under mild assumptions this means that it is determined up to homotopy type by its fundamental group. A famous conjecture of Borel states that closed aspherical manifolds are in fact determined up to homeomorphism by the fundamental group. One could also ask (Borel famously didn’t) whether smooth aspherical manifolds are determined up to diffeomorphism by their fundamental group; this is known to hold in dimensions at most 3 and is false in dimension at least 5. We resolve the remaining case by exhibiting closed smooth aspherical manifolds that are homeomorphic but not diffeomorphic.