{
  "abstract": "Let $M=Ω/Γ$ be a closed properly convex real projective $4$-manifold. We prove the Chern-Hopf-Thurston conjecture for this class of manifolds, i.e. $χ(M)\\geq0$. The argument transfers Akagawa's double-form identity on the Cheng--Yau cone over $Ω$ to a Bochner identity on $M$, from which we deduce that $H^q(M;Λ^pE^*)=0$ whenever $q<p(n+1-p)/(n+1)$, in arbitrary dimension $n$, for some flat bundle $E$ naturally attached to $M$. In dimension four, this implies that the cohomology with coefficients in $Λ^2E^*$ concentrates in degree two.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.31085",
  "author_total": 1,
  "authors": [
    {
      "name": "Andrea Tamburelli"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/4jfabjkmjmbp3.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.31085",
  "fulltext_url": null,
  "id": "4jfabjkmjmbp3",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.31085",
  "language": null,
  "licence": "CC-BY-4.0",
  "licence_label": "CC BY 4.0",
  "licence_source": "article",
  "licence_url": "http://creativecommons.org/licenses/by/4.0/",
  "metadata_licence": "CC0-1.0",
  "native_subjects": [
    [
      "arxiv",
      "math.GT"
    ],
    [
      "openalex",
      "2608|Geometric and Algebraic Topology"
    ]
  ],
  "openalex": "W7223301585",
  "pdf_url": "https://arxiv.org/pdf/2610.31085",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-22",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/4jfabjkmjmbp3.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:34:38Z",
      "native_id": "2610.31085",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.31085"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.GT",
      "subfield": "geometry-topology"
    }
  ],
  "title": "Euler characteristic and flat cohomology of convex projective $4$-manifolds",
  "title_text": "Euler characteristic and flat cohomology of convex projective $4$-manifolds",
  "type": "preprint",
  "updated_at": "2026-10-30T12:34:38Z",
  "url": "https://research.draconitic.com/paper/4jfabjkmjmbp3",
  "venue": "arXiv",
  "versions": []
}