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.
Original languageEnglish
JournalJournal of the American Mathematical Society
DOIs
Publication statusPublished - 24 Jun 2021

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