{
  "abstract": "Asymptotic cohomology was recently introduced to study stability problems in group theory. This paper studies vanishing and Hausdorffness questions around asymptotic cohomology. Our first main result is that, in a fixed degree and for a fixed asymptotic coefficient module, vanishing of asymptotic cohomology is equivalent to vanishing of reduced asymptotic cohomology. In the special case of diagonal coefficient modules, we also obtain a full characterisation of vanishing in terms of bounded cohomology. Our second main result is that asymptotic cohomology vanishes in degree 1 for uniformly convex asymptotic Banach modules. From this, we can deduce Hausdorffness of degree-2 bounded cohomology under the same uniform convexity assumption.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.29872",
  "author_total": 2,
  "authors": [
    {
      "name": "Alexis Marchand"
    },
    {
      "name": "Piotr W. Nowak"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/7a8tbfpzb9zjb.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.29872",
  "fulltext_url": null,
  "id": "7a8tbfpzb9zjb",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.29872",
  "language": null,
  "licence": "CC-BY-NC-ND-4.0",
  "licence_label": "CC BY-NC-ND 4.0",
  "licence_source": "article",
  "licence_url": "http://creativecommons.org/licenses/by-nc-nd/4.0/",
  "metadata_licence": "CC0-1.0",
  "native_subjects": [
    [
      "arxiv",
      "math.GR"
    ],
    [
      "arxiv",
      "math.RT"
    ],
    [
      "openalex",
      "2610|Advanced Operator Algebra Research"
    ]
  ],
  "openalex": "W7214388624",
  "pdf_url": "https://arxiv.org/pdf/2609.29872",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-24",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/7a8tbfpzb9zjb.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:24:15Z",
      "native_id": "2609.29872",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.29872"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.GR",
      "subfield": "algebra-number-theory"
    }
  ],
  "title": "On vanishing and Hausdorffness of asymptotic cohomology",
  "title_text": "On vanishing and Hausdorffness of asymptotic cohomology",
  "type": "preprint",
  "updated_at": "2026-10-30T12:24:15Z",
  "url": "https://research.draconitic.com/paper/7a8tbfpzb9zjb",
  "venue": "arXiv",
  "versions": []
}