{
  "abstract": "Let $G$ be a compact, connected, simply connected semisimple Lie group with Weyl group $W$ and simple reflections $S$. For a simplicial complex $\\mathcal K$ on $S$, form the homotopy colimit $X_{\\mathcal K}(G)=\\operatorname*{hocolim}_{I\\in\\mathcal K}G/G_I$ of standard partial flag manifolds. We compute its integral homology. If $\\operatorname{Des}_R(w)$ is the right descent set of $w\\in W$ and $\\ell(w)$ its Coxeter length, then $$ H_n(X_{\\mathcal K}(G);\\mathbb Z)\\cong \\bigoplus_{w\\in W}\\widetilde H_{n-2\\ell(w)-1}(\\mathcal K_{\\operatorname{Des}_R(w)};\\mathbb Z). $$ Thus the induced subcomplexes of $\\mathcal K$ supply the topological data, while the Weyl group determines which subcomplex occurs and the Schubert-degree shift. The proof gives a chain-level splitting and an integral Morse reduction. We derive homotopy detection, duality and rigidity results, and recover polyhedral products, matroid--Tutte formulas, and the adjoint sphere as special cases.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.01882",
  "author_total": 1,
  "authors": [
    {
      "name": "Yifan Zhang"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/cgwaf4zpjpnjr.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.01882",
  "fulltext_url": null,
  "id": "cgwaf4zpjpnjr",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.01882",
  "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.AT"
    ],
    [
      "arxiv",
      "math.CO"
    ],
    [
      "openalex",
      "2610|Homotopy and Cohomology in Algebraic Topology"
    ]
  ],
  "openalex": "W7207597086",
  "pdf_url": "https://arxiv.org/pdf/2609.01882",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-24",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/cgwaf4zpjpnjr.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:24:15Z",
      "native_id": "2609.01882",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.01882"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.CO",
      "subfield": "combinatorics"
    },
    {
      "field": "mathematics",
      "origin": "arxiv:math.AT",
      "subfield": "geometry-topology"
    }
  ],
  "title": "Parabolic Homotopy Colimits and Coxeter Descents",
  "title_text": "Parabolic Homotopy Colimits and Coxeter Descents",
  "type": "preprint",
  "updated_at": "2026-10-30T12:24:15Z",
  "url": "https://research.draconitic.com/paper/cgwaf4zpjpnjr",
  "venue": "arXiv",
  "versions": []
}