Aut-invariant quasimorphisms on groups
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2023-10
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Journal Article
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Abstract
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 Miklos Abert. The case of graph products of finitely generated abelian groups settles a question of Micha l Marcinkowski. As a consequence, we deduce that a variety of Aut-invariant norms on such groups are unbounded.
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376 (10)
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7307 - 7327
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American Mathematical Society
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08802 - Iozzi, Alessandra (Tit.-Prof.)
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