Diffeomorphism groups and isometry groups in symplectic geometry

08.11. bis 08.11.2019, 10:00  –  Haus 9, Raum 2.22
Arbeitsgruppenseminar Analysis

Steven Rosenberg (Boston University)

It is difficult to say much about the topology of the diffeomorphism group and isometry group of a closed manifold, and few high dimensional results are known.  In work with Staoshi Egi and Yoshi Maeda, we prove that circle bundles N over 4k-dimensional symplectic manifolds have infinite \pi_1(Diff(N)) and \pi_1(Isom(N)).  The infinite order element in these fundamental groups is detected by a Chern-Simons-type class on the loop space LN built from the Wodzicki residue.  This class is calculated by examining some natural Riemannian metrics on LN.