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.