Quasi-morphisms on surface diffeomorphism groups

Jonathan Bowden; Sebastian Hensel; Richard Webb

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arXiv · 1909.07164

Quasi-morphisms on surface diffeomorphism groups

Jonathan Bowden·Sebastian Hensel·Richard Webb

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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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BibTeX RIS

Jonathan Bowden, Sebastian Hensel, Richard Webb. 2019-09-12. Quasi-morphisms on surface diffeomorphism groups. https://arxiv.org/abs/1909.07164

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