{
  "abstract": "We show that for almost every finite dimensional complex representation $W$ of $SO(2)$ the associated complex projective space $\\mathbb{C}P(W)_+$ does not have the rational stable homotopy type of a specific wedge of representation spheres constructed from a chosen filtration of $\\mathbb{C}P(W)_+$. This contrasts with the case for representations of finite Abelian groups where such an equivalence does hold. In the finite group case, the splitting result provides us with a classification result for projective spaces up to rational stable equivalence. In light of the non-splitting as a particular wedge of spheres in the case of projective spaces of $SO(2)$-representations, we also prove a separate classification theorem.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.28039",
  "author_total": 1,
  "authors": [
    {
      "name": "Kian Lush"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/6536xk4hmk268.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.28039",
  "fulltext_url": null,
  "id": "6536xk4hmk268",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.28039",
  "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": "W7223154355",
  "pdf_url": "https://arxiv.org/pdf/2610.28039",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-20",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/6536xk4hmk268.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:34:08Z",
      "native_id": "2610.28039",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.28039"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.AT",
      "subfield": "geometry-topology"
    }
  ],
  "title": "Complex Projective Spaces in Rational $SO(2)$-Equivariant Stable Homotopy Theory",
  "title_text": "Complex Projective Spaces in Rational SO(2)-Equivariant Stable Homotopy Theory",
  "type": "preprint",
  "updated_at": "2026-10-30T12:34:08Z",
  "url": "https://research.draconitic.com/paper/6536xk4hmk268",
  "venue": "arXiv",
  "versions": []
}