{
  "abstract": "Let $X$ be a closed, smooth, orientable, positive definite $4$-manifold with $H_1(X ; \\mathbb{Z}) = 0$. Let $p$ be a prime and suppose that $G = \\mathbb{Z}_p$ acts smoothly on $X$ (if $p=2$ we also require an assumption on how $G$ acts on $H^2(X ; \\mathbb{Z})$). Using equivariant Yang--Mills theory, Hambleton--Lee and Hambleton--Tanase proved (in the simply-connected case) that the fixed point set and tangential isotropy representations coincide with that of an equivariant connected sum of copies of $\\mathbb{CP}^2$ on which $G$ acts linearly. We give a new proof of this result using equivariant Seiberg--Witten theory. Furthermore we also determine the weights of all equivariant line bundles on $X$, showing that these likewise coincide with that of an equivariant connected sum of linear actions on $\\mathbb{CP}^2$.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.14328",
  "author_total": 1,
  "authors": [
    {
      "name": "David Baraglia"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/9fmbzm9q08fct.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.14328",
  "fulltext_url": null,
  "id": "9fmbzm9q08fct",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.14328",
  "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.DG"
    ],
    [
      "arxiv",
      "math.GT"
    ],
    [
      "openalex",
      "2608|Geometric and Algebraic Topology"
    ]
  ],
  "openalex": "W7213237512",
  "pdf_url": "https://arxiv.org/pdf/2609.14328",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-13",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/9fmbzm9q08fct.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:21:29Z",
      "native_id": "2609.14328",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.14328"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.DG",
      "subfield": "geometry-topology"
    }
  ],
  "title": "Weights of finite cyclic actions on definite $4$-manifolds",
  "title_text": "Weights of finite cyclic actions on definite $4$-manifolds",
  "type": "preprint",
  "updated_at": "2026-10-30T12:21:29Z",
  "url": "https://research.draconitic.com/paper/9fmbzm9q08fct",
  "venue": "arXiv",
  "versions": []
}