Families of diffeomorphisms of 4-manifolds via graph surgery
Speaker:
Tadayuki Watanabe, Shimane University
Date and Time:
Monday, July 8, 2019 - 3:30pm to 4:30pm
Location:
Fields Institute, Room 230
Abstract:
In this talk, I will explain a method to construct families of diffeomorphisms of a 4-manifold by using a 4D analogue of Goussarov-Habiro's theory of graph surgery in 3D. Our graph surgery would produce lots of potentially nontrivial elements of homotopy groups of diffeomorphism groups of 4-manifolds. In particular, by evaluating Kontsevich's characteristic classes on our constructions for the 4-sphere, we obtain a negative answer to the 4D analogue of the Smale conjecture.