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

Research output: Contribution to journal › Article › peer-review

3 Citations (Scopus)

8 Downloads (Pure)

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
Pages (from-to)	475–493
Number of pages	19
Journal	Annales mathématiques du Québec
Volume	47
Early online date	3 Dec 2021
DOIs	https://doi.org/10.1007/s40316-021-00184-4
Publication status	Published - 1 Oct 2023

Bibliographical note

Acknowledgements
I like to thank Jarek Ke ̨dra and Benjamin Martin for their continued support and all their helpful com- ments. This work was partly funded by the Leverhulme Trust Research Project Grant RPG-2017-159.

Keywords

Aut-invariant
Quasimorphism
Free product
Stable commutator length

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Cite this

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Aut-invariant quasimorphisms on free products

Abstract

Bibliographical note

Keywords

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