Quasi-morphisms on surface diffeomorphism groups

Bowden, Jonathan; Hensel, Sebastian; Webb, Richard

doi:10.1090/jams/981

Quasi-morphisms on surface diffeomorphism groups
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by Jonathan Bowden, Sebastian Wolfgang Hensel and Richard Webb

J. Amer. Math. Soc. 35 (2022), 211-231

DOI: https://doi.org/10.1090/jams/981

Published electronically: June 24, 2021

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Abstract:

We show that the identity component of the group of diffeomorphisms of a closed oriented surface of positive genus admits many unbounded quasi-morphisms. As a corollary, we also deduce that this group is not uniformly perfect and its fragmentation norm is unbounded, answering a question of Burago–Ivanov–Polterovich. As a key tool we construct a hyperbolic graph on which these groups act, which is the analog of the curve graph for the mapping class group.

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