[Geometry, Topology and Dynamics Seminar] Some exotic nontrivial elements of the rational homotopy groups of Diff(S^4) by Dr. Tadayuki Watanabe (Shimane University)

Abstract: The rational homotopy groups of the group Diff(S^4) of self-diffeomorphisms of S^4 with the C^\infty-topology. We present a method to prove that there are many 'exotic' non-trivial elements in the rational homotopy groups of Diff(S^4) parametrized by trivalent graphs. The proof utilizes Kontsevich's characteristic classes for smooth disk bundles and a version of clasper surgery for families. In fact, these are analogues of Chern-Simons perturbation theory in 3-dimension and clasper theory due to Goussarov and Habiro.