T. Watanabe (Department of Mathematical Sciences, Shimane University)
Title: Some exotic nontrivial elements of the rational homotopy groups of Diff(S^4)
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.