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arXiv · 2103.01354

Aut-invariant quasimorphisms on free products

Bastien Karlhofer
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Abstract

Let $G=A \ast B$ be a free product of freely indecomposable groups. We explicitly construct quasimorphisms on $G$ which are invariant with respect to all automorphisms of $G$. We also prove that the space of such quasimorphisms is infinite-dimensional whenever $G$ is not the infinite dihedral group. As an application we prove that an invariant analogue of stable commutator length recently introduced by Kawasaki and Kimura is non-trivial for these groups.

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Bastien Karlhofer. 2021-03-01. Aut-invariant quasimorphisms on free products. https://arxiv.org/abs/2103.01354

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