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Journal of the American Mathematical Society

Published by the American Mathematical Society, the Journal of the American Mathematical Society (JAMS) is devoted to research articles of the highest quality in all areas of pure and applied mathematics.

ISSN 1088-6834 (online) ISSN 0894-0347 (print)

The 2020 MCQ for Journal of the American Mathematical Society is 4.79.

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Quasi-morphisms on surface diffeomorphism groups
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by Jonathan Bowden, Sebastian Wolfgang Hensel and Richard Webb HTML | PDF
J. Amer. Math. Soc. 35 (2022), 211-231

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.
References
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Additional Information
  • Jonathan Bowden
  • Affiliation: Mathematisches Institut, Universität Regensburg, Universitätsstraße 31, 93053 Regensburg, Germany
  • MR Author ID: 873123
  • Email: jonathan.bowden@ur.de
  • Sebastian Wolfgang Hensel
  • Affiliation: Mathematisches Institut der Universität München, Theresienstraße 39, 80333 München, Germany
  • MR Author ID: 938076
  • ORCID: 0000-0002-9369-4173
  • Email: hensel@math.lmu.de
  • Richard Webb
  • Affiliation: Department of Mathematics, The University of Manchester, Oxford Road, Manchester, M13 9PL, United Kingdom
  • MR Author ID: 1104740
  • ORCID: 0000-0001-9161-0928
  • Email: richard.webb@manchester.ac.uk
  • Received by editor(s): March 30, 2020
  • Received by editor(s) in revised form: January 31, 2021, and March 17, 2021
  • Published electronically: June 24, 2021
  • Additional Notes: The first and second authors were supported by the Special Priority Programme SPP 2026 Geometry at Infinity funded by the DFG. The third author was supported by the EPSRC Fellowship EP/N019644/2.

  • Dedicated: Dedicated to Mladen Bestvina on the occasion of his 60th birthday.
  • © Copyright 2021 by the authors
  • Journal: J. Amer. Math. Soc. 35 (2022), 211-231
  • MSC (2020): Primary 20F65, 57Sxx
  • DOI: https://doi.org/10.1090/jams/981
  • MathSciNet review: 4322392