Title: Symmetries of exotic negatively curved manifolds
Speaker: Bena Tshishiku (Harvard University)
Abstract: This talk is centered around the following question: given a smooth manifold N that is homeomorphic but not diffeomorphic to a hyperbolic manifold M, how much symmetry does N have? For example, does Isom(M) act on N by diffeomorphisms? Farrell-Jones showed that in general the answer is "No"; however, for their examples, it is still possible for the orientation-preserving subgroup to act on N. In this talk, we will discuss this problem and its relation to Nielsen realization. The main result is a construction of examples of N such that Isom(M) does act on N, as well as examples where the largest subgroup of Isom(M) that acts on N has arbitrarily large index. This is joint work with Mauricio Bustamante.
