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 |
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Pages (from-to) | 475–493 |
Number of pages | 19 |
Journal | Annales mathématiques du Québec |
Volume | 47 |
Early online date | 3 Dec 2021 |
DOIs | |
Publication status | Published - 1 Oct 2023 |
Bibliographical note
AcknowledgementsI 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