Olga Aryasova (Inst. of Geophysics, Nat. Acad. of Sciences of Ukraine / Friedrich–Schiller–Univ. Jena)
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.