{
  "abstract": "Bouc's hook cycles span the rational top homology of the matching complex of $K_{2k+1}$. We prove that their integral saturation quotient has exponent exactly $2^{\\lfloor k/2\\rfloor}$ for every $k\\geq1$, and construct divided-power cycles attaining this bound. For $k\\geq2$, the homology lattice is not isomorphic to the standard integral hook lattice as an $\\mathfrak S_{2k+1}$-module. For circulant complexes, we determine the integral dihedral homology modules of $\\operatorname{Ind}(C_{3s}^{s-1})$, $\\operatorname{Ind}(C_{3s+1}^{s-1})$ and $\\operatorname{Ind}(C_{3s+2}^{s-1})$, for $s\\geq3$, $s\\geq2$ and $s\\geq3$, respectively, and classify the least scalar lifts of all primitive equivariant quotients to the rank-one module with trivial rotation and negative reflection. Tate localization relates prime-order gluing to fixed-point homology under a free, single-degree homology hypothesis. Explicit cycle subgroups separate saturation defects from obstructions to equivariant sections. For circulant independence complexes with jumps two and three, we prove an eight-periodic ordinary homotopy classification and a fixed-space obstruction to uniform representation suspensions. For every fixed nonempty bounded positive jump set, a finite-state construction gives a rational critical-face series.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.22082",
  "author_total": 2,
  "authors": [
    {
      "name": "Qihang Wang"
    },
    {
      "name": "Weiye Li"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/3ytt9m742gy0v.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.22082",
  "fulltext_url": null,
  "id": "3ytt9m742gy0v",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.22082",
  "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.AT"
    ],
    [
      "arxiv",
      "math.CO"
    ],
    [
      "openalex",
      "2610|Homotopy and Cohomology in Algebraic Topology"
    ]
  ],
  "openalex": "W7222395934",
  "pdf_url": "https://arxiv.org/pdf/2610.22082",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-15",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/3ytt9m742gy0v.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:29:54Z",
      "native_id": "2610.22082",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.22082"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.CO",
      "subfield": "combinatorics"
    },
    {
      "field": "mathematics",
      "origin": "arxiv:math.AT",
      "subfield": "geometry-topology"
    }
  ],
  "title": "Integral homology lattices of matching and circulant complexes",
  "title_text": "Integral homology lattices of matching and circulant complexes",
  "type": "preprint",
  "updated_at": "2026-10-30T12:29:54Z",
  "url": "https://research.draconitic.com/paper/3ytt9m742gy0v",
  "venue": "arXiv",
  "versions": []
}