{
  "id": "2201.07176",
  "version": "v2",
  "published": "2022-01-18T18:22:15.000Z",
  "updated": "2022-02-07T16:02:11.000Z",
  "title": "Almost Complex Structures on Homotopy Complex Projective Spaces",
  "authors": [
    "Keith Mills"
  ],
  "comment": "17 pages. Replaces an earlier version with very minor changes concerning the classification of homotopy complex projective spaces",
  "categories": [
    "math.GT",
    "math.AT"
  ],
  "abstract": "We completely answer the question of when a homotopy $\\mathbb{C}P^n$, a smooth closed manifold with the oriented homotopy type of $\\mathbb{C}P^n$, admits an almost complex structure for $3 \\leq n \\leq 6$. For $3 \\leq n \\leq 5$ all homotopy $\\mathbb{C}P^n$s admit almost complex structures, while for $n=6$ there exist homotopy $\\mathbb{C}P^n$s that do not. Our methods provide a new proof of a result of Libgober and Wood on the classification of almost complex structures on homotopy $\\mathbb{C}P^4$s.",
  "revisions": [
    {
      "version": "v2",
      "updated": "2022-02-07T16:02:11.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "57R15",
      "57R20",
      "32Q60",
      "19L64"
    ],
    "keywords": [
      "homotopy complex projective spaces",
      "complex structure",
      "smooth closed manifold",
      "oriented homotopy type",
      "classification"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 17,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}