{
  "abstract": "Let $X$ be a $(q-1)$-connected rational space of finite type, where $q\\ge2$, with homotopical nilpotency $nil_h(X)=n\\ge1$. If $H^{>N}(X;Q)=0$ and $N\\le q(n+3)-3$, we prove that $Hnil(X)=n$. More precisely, the sufficient bound is $N\\le a_n(M_X)+2q-3$, where $a_n(M_X)$ is the first nonzero internal cohomology degree of $(M_X^+)^{n+1}$ in the minimal model. A family of examples proves that the constant $-3$ in this refined bound is optimal; optimality of the uniform bound is not asserted. The proof uses two stages of adjoining primitives to an ideal of the fixed minimal model.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.06518",
  "author_total": 1,
  "authors": [
    {
      "name": "Paul-Eugene Parent"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/10wm87jnc95bk.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.06518",
  "fulltext_url": null,
  "id": "10wm87jnc95bk",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.06518",
  "language": null,
  "licence": "CC-BY-NC-ND-4.0",
  "licence_label": "CC BY-NC-ND 4.0",
  "licence_source": "article",
  "licence_url": "http://creativecommons.org/licenses/by-nc-nd/4.0/",
  "metadata_licence": "CC0-1.0",
  "native_subjects": [
    [
      "arxiv",
      "math.AT"
    ],
    [
      "openalex",
      "2610|Homotopy and Cohomology in Algebraic Topology"
    ]
  ],
  "openalex": "W7212035173",
  "pdf_url": "https://arxiv.org/pdf/2609.06518",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-06",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/10wm87jnc95bk.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:19:58Z",
      "native_id": "2609.06518",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.06518"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.AT",
      "subfield": "geometry-topology"
    }
  ],
  "title": "Homotopical Nilpotency and Homology Nilpotency: A Dimension--Connectivity Bound",
  "title_text": "Homotopical Nilpotency and Homology Nilpotency: A Dimension--Connectivity Bound",
  "type": "preprint",
  "updated_at": "2026-10-30T12:19:58Z",
  "url": "https://research.draconitic.com/paper/10wm87jnc95bk",
  "venue": "arXiv",
  "versions": []
}