{
  "abstract": "Let $\\mathcal{F}$ be a saturated fusion system over a finite $p$-group $S$, and $\\mathcal{O}^c (\\mathcal{F})$ denote the centric orbit category of $\\mathcal{F}$. Suppose that $G$ is a discrete group realizing $\\mathcal{F}$, and $\\mathcal{C}$ is the collection of all $p$-centric subgroups in $G$. We prove that for every $\\mathbb{Z}_{(p)} \\mathcal{O} ^c (\\mathcal{F})$-module $M$, the higher limits $\\lim ^* _{\\mathcal{O}^c (\\mathcal{F})} M$ are isomorphic to the equivariant cohomology $H_ G ^* (|\\mathcal{C}| ; \\mathcal{M} )$, where $\\mathcal{M}$ is the $G$-equivariant coefficient system on $|\\mathcal{C}|$ induced by $M$. This is the fusion system version of a theorem by Grodal for higher limits over the $p$-orbit category $\\mathcal{O}_p(G)$ of a finite group $G$. As a consequence, for every fusion system $\\mathcal{F}$, we obtain a finite sequence of cohomology groups, involving the cohomology of $\\mathcal{F}$, which is exact if and only if the mod-$p$ subgroup decomposition for $\\mathcal{F}$ over $\\mathcal{F}$-centric subgroups is sharp.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.40915",
  "author_total": 1,
  "authors": [
    {
      "name": "Ergun Yalcin"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/b5xqtnshh9j83.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.40915",
  "fulltext_url": null,
  "id": "b5xqtnshh9j83",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.40915",
  "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.AT"
    ]
  ],
  "openalex": null,
  "pdf_url": "https://arxiv.org/pdf/2610.40915",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-29",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/b5xqtnshh9j83.ris",
  "sources": [
    {
      "first_seen": "2026-11-02T12:21:20Z",
      "native_id": "2610.40915",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.40915"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.AT",
      "subfield": "geometry-topology"
    }
  ],
  "title": "Higher limits over the fusion orbit category via subgroup complexes",
  "title_text": "Higher limits over the fusion orbit category via subgroup complexes",
  "type": "preprint",
  "updated_at": "2026-11-04T15:20:52Z",
  "url": "https://research.draconitic.com/paper/b5xqtnshh9j83",
  "venue": "arXiv",
  "versions": []
}