Kontsevich's characteristic classes and diffeomorphisms of the 4-sphere

Nom de l'orateur
Tadayuki Watanabe
Etablissement de l'orateur
Shimane University
Date et heure de l'exposé
Lieu de l'exposé
Salle Éole

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). This leads, for example, to a negative answer to Eliashberg's problem, which asks if the space of compact-support symplectic structures on R^4 is contractible. In proving our result, we give and use a formula for the characteristic numbers for some bundles which counts gradient flow-graphs in the bundles. This is an analogue of K. Fukaya's Morse homotopy for families.