{
  "abstract": "We study the Goodwillie tower of the identity evaluated at the circle. Our main result is the p-local equivalence $ΩP_{p^k}I(S^1) \\simeq \\mathbb{Z} \\times Ω^{\\infty+2k}τ_{>0}\\mathbb{Sp}^{p^k}$ obtained from the work of Behrens and Kuhn on the Whitehead conjecture. In particular, this identifies the Goodwillie approximations of the circle as infinite loop spaces, a phenomenon which does not hold in general. The equivalence also reduces the computation of their homotopy groups to a stable problem, making them accessible to tools such as the Adams spectral sequence and to computer calculations. We place these computations in a more general framework by developing a Goodwillie-calculus analogue of the Gray sequence, which relates the homotopy groups of successive stages of the tower.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.31269",
  "author_total": 1,
  "authors": [
    {
      "name": "Marco Nervo"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/56zs8c82t4s80.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.31269",
  "fulltext_url": null,
  "id": "56zs8c82t4s80",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.31269",
  "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.AT"
    ],
    [
      "openalex",
      "2610|Homotopy and Cohomology in Algebraic Topology"
    ]
  ],
  "openalex": "W7214626529",
  "pdf_url": "https://arxiv.org/pdf/2609.31269",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-25",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/56zs8c82t4s80.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:24:57Z",
      "native_id": "2609.31269",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.31269"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.AT",
      "subfield": "geometry-topology"
    }
  ],
  "title": "An abelian model for the Goodwillie tower of the circle",
  "title_text": "An abelian model for the Goodwillie tower of the circle",
  "type": "preprint",
  "updated_at": "2026-10-30T12:24:57Z",
  "url": "https://research.draconitic.com/paper/56zs8c82t4s80",
  "venue": "arXiv",
  "versions": []
}