{
  "abstract": "We study smooth structures on the topological manifold underlying complex projective space. We conjecture that every complex projective space $\\mathbb{CP}^n$ with $n>3$ admits an exotic smooth structure. We prove two results providing strong evidence for this conjecture. First, the set of complex dimensions $n$ for which $\\mathbb{CP}^n$ admits an exotic smooth structure has natural density one. Second, we explicitly identify $266$ congruence classes modulo $288$ such that $\\mathbb{CP}^n$ admits an exotic smooth structure whenever $n>3$ lies in one of these classes. These classes cover more than $92\\%$ of complex dimensions, improving the previously known lower bound of approximately $36\\%$. We prove these results by first relating the concordance group of $\\mathbb{CP}^n$ to suitable Atiyah--Hirzebruch filtration subgroups of its stable cohomotopy group, and then applying computations in chromatic homotopy theory at height $2$.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2611.08406",
  "author_total": 3,
  "authors": [
    {
      "name": "Yueshi Hou"
    },
    {
      "name": "Hana Jia Kong"
    },
    {
      "name": "Zhouli Xu"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/eem2twb783jsq.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2611.08406",
  "fulltext_url": null,
  "id": "eem2twb783jsq",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2611.08406",
  "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.AT"
    ]
  ],
  "openalex": null,
  "pdf_url": "https://arxiv.org/pdf/2611.08406",
  "pmcid": null,
  "pmid": null,
  "published": "2026-11-05",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/eem2twb783jsq.ris",
  "sources": [
    {
      "first_seen": "2026-11-06T18:21:34Z",
      "native_id": "2611.08406",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2611.08406"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.AT",
      "subfield": "geometry-topology"
    }
  ],
  "title": "Exotic smooth structures on complex projective spaces",
  "title_text": "Exotic smooth structures on complex projective spaces",
  "type": "preprint",
  "updated_at": "2026-11-06T18:21:34Z",
  "url": "https://research.draconitic.com/paper/eem2twb783jsq",
  "venue": "arXiv",
  "versions": []
}