{
  "abstract": "Homology nilpotency of a simply connected minimal Sullivan algebra $M$ is the least integer $n$ for which $(M^+)^{n+1}$ is contained in an acyclic differential ideal. We develop lower- and upper-bound criteria, including methods for rational cell attachments, and construct an explicit finite-type minimal Sullivan algebra $M$ satisfying $nil_h(M)=3<Hnil(M)=4$. Complete strictly coordinated retractive towers identify the obstruction: they characterize homotopical nil-length while exposing the additional quotient defect measured by homology nilpotency. We then show that this rigid defect disappears after stabilization by degreewise finite wedges of simply connected rational spheres: $$ Hnil_s(X)=cat_o(X) $$ for every simply connected rational space $X$ of finite type.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.02980",
  "author_total": 1,
  "authors": [
    {
      "name": "Paul-Eugène Parent"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/d6sghs3evzfwn.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.02980",
  "fulltext_url": null,
  "id": "d6sghs3evzfwn",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.02980",
  "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": "W7208731747",
  "pdf_url": "https://arxiv.org/pdf/2609.02980",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-02",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/d6sghs3evzfwn.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:18:36Z",
      "native_id": "2609.02980",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.02980"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.AT",
      "subfield": "geometry-topology"
    }
  ],
  "title": "Homology Nilpotency in Rational Homotopy Theory: Cell Attachments, Retractive Towers, Divergence, and Stabilization",
  "title_text": "Homology Nilpotency in Rational Homotopy Theory: Cell Attachments, Retractive Towers, Divergence, and Stabilization",
  "type": "preprint",
  "updated_at": "2026-10-30T12:18:36Z",
  "url": "https://research.draconitic.com/paper/d6sghs3evzfwn",
  "venue": "arXiv",
  "versions": []
}