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Transactions of the American Mathematical Society

Published by the American Mathematical Society since 1900, Transactions of the American Mathematical Society is devoted to longer research articles in all areas of pure and applied mathematics.

ISSN 1088-6850 (online) ISSN 0002-9947 (print)

The 2020 MCQ for Transactions of the American Mathematical Society is 1.48.

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$\operatorname {Aut}$-invariant quasimorphisms on groups
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by Francesco Fournier-Facio and Richard D. Wade
Trans. Amer. Math. Soc. 376 (2023), 7307-7327
Published electronically: June 21, 2023


For a large class of groups, we exhibit an infinite-dimensional space of homogeneous quasimorphisms that are invariant under the action of the automorphism group. This class includes non-elementary hyperbolic groups, infinitely-ended finitely generated groups, some relatively hyperbolic groups, and a class of graph products of groups that includes all right-angled Artin and Coxeter groups that are not virtually abelian.

This was known for $F_2$ by a result of Brandenbursky and Marcinkowski [Comment. Math. Helv. 94 (2019), pp. 661–687], but is new even for free groups of higher rank, settling a question of Miklós Abért. The case of graph products of finitely generated abelian groups settles a question of Michał Marcinkowski. As a consequence, we deduce that a variety of $Aut$-invariant norms on such groups are unbounded.

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Bibliographic Information
  • Francesco Fournier-Facio
  • Affiliation: Department of Mathematics, ETH Zürich, Switzerland
  • MR Author ID: 1532652
  • ORCID: 0000-0003-0386-2071
  • Email:
  • Richard D. Wade
  • Affiliation: Mathematical Institute, Oxford University, United Kingdom
  • MR Author ID: 951412
  • ORCID: 0000-0001-9274-3474
  • Email:
  • Received by editor(s): February 18, 2023
  • Received by editor(s) in revised form: April 28, 2023, and May 4, 2023
  • Published electronically: June 21, 2023
  • Additional Notes: The second author was funded by The Royal Society through a University Research Fellowship.
  • © Copyright 2023 American Mathematical Society
  • Journal: Trans. Amer. Math. Soc. 376 (2023), 7307-7327
  • MSC (2020): Primary 20F65, 20E36; Secondary 20F67, 20J05
  • DOI:
  • MathSciNet review: 4636691