{
  "abstract": "Let $M$ be a compact connected oriented smooth manifold, of dimension $n\\ge2$. Let $\\mathcal T_MG$ be one of the following transformation groups: $Homeo_0(M,μ)$, $Diff_0(M,μ)$, $Symp_0(M, ω)$ (in case $M$ is symplectic) and $Ham(M, ω)$ (in case $M$ is symplectic). Denote by $\\overline{H}_b^d(\\mathcal T_M)$ reduced bounded cohomology of $\\mathcal T_M$ in degree $d$, and by $\\overline{EH}^d(\\mathcal T_M)$ reduced exact bounded cohomology of $\\mathcal T_M$ in degree $d$. In this paper we prove that if $n=2$ and $M$ is a closed surface $Σ_g$ or a disc $\\mathbb D$, then for every $d\\ge 2$ $$\\dim(\\overline{H}b^d(\\mathcal T_M))=\\infty.$$ Moreover, $\\dim\\overline{EH}^d(\\mathcal T_M)=\\infty$ if $\\mathcal T_M$ is either $Diff_0(Σ_g,μ)$ or $Ham(Σ_g, ω)$, or $Ham(\\mathbb{D}, ω)$; or $g>1$. In case $n>2$, under certain conditions on $π_1(M)$, we prove that for every degree $d\\ge 2$ $$\\dim\\overline{EH}^d(\\mathcal T_M)=\\infty.$$ In particular, these results hold for $\\mathcal T_M$ when $M$ is a closed, orientable smooth manifold admitting a Riemannian metric of strictly negative sectional curvature of an arbitrary dimension.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.11327",
  "author_total": 1,
  "authors": [
    {
      "name": "Michael Brandenbursky"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/4yxndbwwk38jb.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.11327",
  "fulltext_url": null,
  "id": "4yxndbwwk38jb",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.11327",
  "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",
      "2608|Geometric and Algebraic Topology"
    ]
  ],
  "openalex": "W7221109903",
  "pdf_url": "https://arxiv.org/pdf/2610.11327",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-08",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/4yxndbwwk38jb.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:27:58Z",
      "native_id": "2610.11327",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.11327"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.GR",
      "subfield": "algebra-number-theory"
    },
    {
      "field": "mathematics",
      "origin": "arxiv:math.GT",
      "subfield": "geometry-topology"
    }
  ],
  "title": "Bounded cohomology of transformation groups in all degrees",
  "title_text": "Bounded cohomology of transformation groups in all degrees",
  "type": "preprint",
  "updated_at": "2026-10-30T12:27:58Z",
  "url": "https://research.draconitic.com/paper/4yxndbwwk38jb",
  "venue": "arXiv",
  "versions": []
}