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Quasi-morphisms on surface diffeomorphism groups

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Sebastian Hensel
LMU München
Thu, 23/01/2020 - 16:30 - 17:30
MPIM Lecture Hall

We will construct nontrivial quasimorphisms on the group of diffeomorphisms of a surface of
genus at least 2 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 Diff0(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.

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