{
  "abstract": "Using the strong discrete Morse theory developed by Fernández, we define the complex $\\mathcal{SM}(K)$ of strong discrete Morse matchings on a simplicial complex $K$, as well as the pure subcomplex $\\mathcal{SM}_{pure}(K)$ generated by the facets in $\\mathcal{SM}(K)$ of maximal dimension. For most complexes $K$ these objects are proper subcomplexes of the complexes ${\\mathfrak M}(K)$ and ${\\mathfrak M}_{\\textrm{pure}}(K)$ defined by Chari--Joswig using all Morse matchings on $K$. The homotopy types of the latter are not well-understood in general, but they are known when $K$ is the path $P_n$ with $n$ edges, the cycle $C_n$ with $n$ edges, the star $S_n$ with $n$ leaves, the $n$-simplex $Δ^n$ ($n\\le 3$), and the boundary $\\partialΔ^n$ ($n\\le 3$). in this paper we compute the homotopy types of $\\mathcal{SM}_{pure}(C_n)$ and $\\mathcal{SM}(K)$ for $K=P_n,S_n,Δ^n,\\partialΔ^n$ for all $n$. We also compute the homology of $\\mathcal{SM}(C_n)$ for $n\\le 21$.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.06844",
  "author_total": 2,
  "authors": [
    {
      "name": "Kevin Knudson"
    },
    {
      "name": "Abigail Owens-White"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/d8whcbs50j4f6.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.06844",
  "fulltext_url": null,
  "id": "d8whcbs50j4f6",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.06844",
  "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",
      "2607|Advanced Combinatorial Mathematics"
    ]
  ],
  "openalex": "W7212006277",
  "pdf_url": "https://arxiv.org/pdf/2609.06844",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-06",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/d8whcbs50j4f6.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:19:58Z",
      "native_id": "2609.06844",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.06844"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.CO",
      "subfield": "combinatorics"
    },
    {
      "field": "mathematics",
      "origin": "arxiv:math.AT",
      "subfield": "geometry-topology"
    }
  ],
  "title": "Complexes of strong discrete Morse matchings",
  "title_text": "Complexes of strong discrete Morse matchings",
  "type": "preprint",
  "updated_at": "2026-10-30T12:19:58Z",
  "url": "https://research.draconitic.com/paper/d8whcbs50j4f6",
  "venue": "arXiv",
  "versions": []
}