Aut-invariant quasimorphisms on groups

Journal article

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 F2 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.

Authors: Fournier-Facio, F; Wade, RD

• Publication status: Published
• Peer review status: Peer reviewed
• Publisher: American Mathematical Society
• Journal: Transactions of the American Mathematical Society
• Volume: 376
• Pages: 7307-7327
• Publication date: 2023-06-21
• Acceptance date: 2023-05-05
• DOI: 10.1090/tran/8980
• EISSN: 1088-6850
• ISSN: 0002-9947
• Language: English
• Keywords: FFR