Berkeley topology seminar

Wednesdays at 4pm in 3 Evans Hall

organizers: Ian Agol and Siddhi Krishna

Danny Ruberman: Closed exotic aspherical 4-manifolds

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 their fundamental group. One could also ask (although 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 to be false in dimension at least 5. We resolve the remaining case by exhibiting closed smooth aspherical 4-manifolds that are homeomorphic but not diffeomorphic. This is joint with Davis, Hayden, Huang, and Sunukjian.