QUASI-MORPHISMS ON SURFACE DIFFEOMORPHISM GROUPS

Jonathan  Bowden; Sebastian  Hensel; Richard Webb

doi:10.1090/jams/981

QUASI-MORPHISMS ON SURFACE DIFFEOMORPHISM GROUPS

Jonathan Bowden , Sebastian Hensel, Richard Webb

Pure Mathematics

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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 language	English
Journal	Journal of the American Mathematical Society
DOIs	https://doi.org/10.1090/jams/981
Publication status	Published - 24 Jun 2021

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quasi-morphisms on surface diffeomorphism groupsAccepted author manuscript, 380 KB

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title = "QUASI-MORPHISMS ON SURFACE DIFFEOMORPHISM GROUPS",

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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AB - 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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JO - Journal of the American Mathematical Society

JF - Journal of the American Mathematical Society

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QUASI-MORPHISMS ON SURFACE DIFFEOMORPHISM GROUPS

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