07/13: Sebastian Hensel

Quasi-morphisms on surface diffeomorphism groups

Abstract: We will construct nontrivial quasimorphisms on the group of diffeomorphisms of a surface of genus at least 1 which are isotopic to the identity. This involves considering the graph whose vertices
correspond to curves on the surface (not up to isotopy!), and transferring usual curve graph methods to this setting. In particular, we show that it is hyperbolic, and we construct elements of Diff_0(S) which act as independent enough hyperbolic elements on it. As a consequence, we also solve a question by Burago-Ivanov-Polterovich on the unboundedness of the fragmentation norm. This is joint work with Jonathan Bowden and Richard Webb.