Aut-invariant quasimorphisms on free products

Bastien Daniel Karlhofer

doi:10.1007/s40316-021-00184-4

Aut-invariant quasimorphisms on free products

Bastien Daniel Karlhofer^* (Corresponding Author)

^*Corresponding author for this work

School of Natural & Computing Sciences

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Abstract

Let G = A ∗ 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.

Original language	English
Number of pages	19
Journal	Annales mathématiques du Québec
Early online date	3 Dec 2021
DOIs	https://doi.org/10.1007/s40316-021-00184-4
Publication status	E-pub ahead of print - 3 Dec 2021

Keywords

Aut-invariant
Quasimorphism
Free product
Stable commutator length

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10.1007/s40316-021-00184-4Licence: CC BY

https://arxiv.org/abs/2103.01354Licence: CC BY

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N2 - Let G = A ∗ 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.

AB - Let G = A ∗ 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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Aut-invariant quasimorphisms on free products

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