{
  "id": "2103.01354",
  "version": "v1",
  "published": "2021-03-01T23:43:01.000Z",
  "updated": "2021-03-01T23:43:01.000Z",
  "title": "Aut-invariant quasimorphisms on free products",
  "authors": [
    "Bastien Karlhofer"
  ],
  "comment": "17 pages",
  "categories": [
    "math.GR"
  ],
  "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.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2021-03-01T23:43:01.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "20F65",
      "20E06"
    ],
    "keywords": [
      "free product",
      "aut-invariant quasimorphisms",
      "infinite dihedral group",
      "explicitly construct quasimorphisms",
      "invariant analogue"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 17,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}