{
  "abstract": "We study unitary \\(S^1\\)-manifolds with four isolated fixed points in relation to Kosniowski's conjectural inequality \\(4χ(M)>\\dim M\\). For every integer \\(m\\ge3\\), we show that there exists a unitary \\(S^1\\)-manifold \\(M_m^{18}\\) with exactly four isolated fixed points, and these manifolds are pairwise distinct and nonzero in ordinary complex bordism. Since \\(χ(M_m^{18})=4\\), they give an infinite family of counterexamples to \\(4χ(M)>\\dim M\\). By gluing two blocks formed by \\(G_2/SU(3)\\cong S^6\\) and the unit disk $D(V)$ of 12- dimensional real $S^1$-representation $V$ along their equivariantly identified free boundaries, we explicitly construct such a manifold $M^{18}_3$. We also prove that the four-point case is null-bordant in real dimension \\(16\\) and in every real dimension greater than \\(18\\); hence \\(18\\) is the smallest dimension in which such a counterexample occurs.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.23855",
  "author_total": 3,
  "authors": [
    {
      "name": "Zhi Lü"
    },
    {
      "name": "Jun Ma"
    },
    {
      "name": "Qiangbo Tan"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/cb5vfszw1vnc1.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.23855",
  "fulltext_url": null,
  "id": "cb5vfszw1vnc1",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.23855",
  "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",
      "2610|Homotopy and Cohomology in Algebraic Topology"
    ]
  ],
  "openalex": "W7222976632",
  "pdf_url": "https://arxiv.org/pdf/2610.23855",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-16",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/cb5vfszw1vnc1.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:30:37Z",
      "native_id": "2610.23855",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.23855"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.AT",
      "subfield": "geometry-topology"
    }
  ],
  "title": "Unitary $S^1$-Manifolds with Four Fixed Points and Kosniowski's Conjecture",
  "title_text": "Unitary S^1-Manifolds with Four Fixed Points and Kosniowski's Conjecture",
  "type": "preprint",
  "updated_at": "2026-10-30T12:33:31Z",
  "url": "https://research.draconitic.com/paper/cb5vfszw1vnc1",
  "venue": "arXiv",
  "versions": []
}