Aut-invariant quasimorphisms on free products

Bastien Daniel Karlhofer* (Corresponding Author)

*Corresponding author for this work

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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 languageEnglish
Pages (from-to)475–493
Number of pages19
JournalAnnales mathématiques du Québec
Early online date3 Dec 2021
Publication statusPublished - 1 Oct 2023

Bibliographical note

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.


  • Aut-invariant
  • Quasimorphism
  • Free product
  • Stable commutator length


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