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.
Kontsevich's characteristic classes and diffeomorphisms of the 4-sphere
- Se connecter pour poster des commentaires
Nom de l'orateur
Tadayuki Watanabe
Etablissement de l'orateur
Shimane University
Date et heure de l'exposé
Lieu de l'exposé
Salle Éole