{
  "abstract": "Let $N_g$ be a closed connected nonorientable surface of genus $g\\ge1$, let $ω$ be a smooth positive density, and let $μ$ be a good measure. In this paper we generalize the Gambaudo--Ghys construction using homogeneous quasimorphisms on the central quotients of the braid groups of $N_g$. We prove injectivity of this map for density-preserving diffeomorphisms. For $g\\ge2$ and quasimorphisms vanishing on the disc braid group, we obtain an injective map to $C^0$-continuous homogeneous quasimorphisms on $Homeo_0(N_g,μ)$. We also obtain undistortion criteria in $Homeo_0(N_g)$ and $Diff_0(N_g)$. For $g=1,2$ and every $d\\ge2$, we prove $$ \\dim\\overline H_b^d(Homeo_0(N_g,μ))=\\infty,\\qquad \\dim\\overline{EH}_b^d(Diff_0(N_g,ω))=\\infty. $$ Moreover, $\\overline{EH}_b^d(Homeo_0(N_2,μ))$ is infinite dimensional in every positive even degree $d$. Here $\\overline{H}_b^d$ and $\\overline{EH}_b^d$ denote reduced bounded cohomology and reduced exact bounded cohomology, respectively.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2611.02847",
  "author_total": 1,
  "authors": [
    {
      "name": "Michael Brandenbursky"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/0trn52cctegsy.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2611.02847",
  "fulltext_url": null,
  "id": "0trn52cctegsy",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2611.02847",
  "language": null,
  "licence": "LicenseRef-arXiv-nonexclusive-1.0",
  "licence_label": "arXiv licence",
  "licence_source": "article",
  "licence_url": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
  "metadata_licence": "CC0-1.0",
  "native_subjects": [
    [
      "arxiv",
      "math.GR"
    ],
    [
      "arxiv",
      "math.GT"
    ],
    [
      "arxiv",
      "math.SG"
    ]
  ],
  "openalex": null,
  "pdf_url": "https://arxiv.org/pdf/2611.02847",
  "pmcid": null,
  "pmid": null,
  "published": "2026-11-02",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/0trn52cctegsy.ris",
  "sources": [
    {
      "first_seen": "2026-11-03T12:21:10Z",
      "native_id": "2611.02847",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2611.02847"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.GR",
      "subfield": "algebra-number-theory"
    },
    {
      "field": "mathematics",
      "origin": "arxiv:math.GT",
      "subfield": "geometry-topology"
    }
  ],
  "title": "Quasimorphisms and bounded cohomology of transformation groups of nonorientable surfaces",
  "title_text": "Quasimorphisms and bounded cohomology of transformation groups of nonorientable surfaces",
  "type": "preprint",
  "updated_at": "2026-11-05T15:20:22Z",
  "url": "https://research.draconitic.com/paper/0trn52cctegsy",
  "venue": "arXiv",
  "versions": []
}