{
  "abstract": "Let $n\\ge5$ be odd and let \\(L_{3q}^n=S^n/C_{3q}\\) be the standard lens space, where $q>3$ is prime. We prove that for all sufficiently large $q$, \\[ σ(L_{3q}^n) > (3q)^{-2/n}Y(S^n)=Y(L_{3q}^n,[g_{\\rm rd}]). \\] Here \\([g_{\\rm rd}]\\) denotes the quotient-round conformal class. Combining spin bordism with the surgery theorem of Ammann--Dahl--Humbert, we establish \\[ σ(L_{3q}^n)\\ge \\min \\{q^{-2/n}Y(S^n),Λ_n\\}, \\] where $Λ_n>0$ depends only on $n$. For sufficiently large $q$, this exceeds the quotient-round value, showing that the quotient-round conformal class need not maximize the smooth Yamabe invariant in any odd dimension $n\\ge5$.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.18662",
  "author_total": 1,
  "authors": [
    {
      "name": "Jakob Loren"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/ag4trrj9296dv.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.18662",
  "fulltext_url": null,
  "id": "ag4trrj9296dv",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.18662",
  "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.DG"
    ],
    [
      "openalex",
      "2604|Geometric Analysis and Curvature Flows"
    ]
  ],
  "openalex": "W7221790554",
  "pdf_url": "https://arxiv.org/pdf/2610.18662",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-13",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/ag4trrj9296dv.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:29:20Z",
      "native_id": "2610.18662",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.18662"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.DG",
      "subfield": "geometry-topology"
    }
  ],
  "title": "Odd-dimensional lens-space Yamabe counterexamples",
  "title_text": "Odd-dimensional lens-space Yamabe counterexamples",
  "type": "preprint",
  "updated_at": "2026-10-30T12:29:20Z",
  "url": "https://research.draconitic.com/paper/ag4trrj9296dv",
  "venue": "arXiv",
  "versions": []
}