Tadayuki Watanabe, Shimane University, Japan

Title: Some exotic nontrivial elements of the rational homotopy groups of Diff(S⁴)

Abstract: Kontsevich's characteristic classes for framed smooth homology sphere bundles were
defined by Kontsevich as a higher dimensional analogue of Chern-Simons perturbation theory in
3-dimension, developed by himself. In this talk, I will present an application of Kontsevich's
characteristic class to a disproof of the 4-dimensional Smale conjecture, which says that the group
of self-diffeomorphisms of the 4-sphere has the same homotopy type as the orthogonal group O(5).