{
  "id": "1712.04572",
  "version": "v1",
  "published": "2017-12-13T00:03:05.000Z",
  "updated": "2017-12-13T00:03:05.000Z",
  "title": "Quotients of $S^2\\times{S^2}$",
  "authors": [
    "I. Hambleton",
    "J. A. Hillman"
  ],
  "comment": "18 pages",
  "categories": [
    "math.GT"
  ],
  "abstract": "We consider closed topological 4-manifolds $M$ with universal cover ${S^2\\times{S^2}}$ and Euler characteristic $\\chi(M) = 1$. All such manifolds with $\\pi=\\pi_1(M)\\cong {\\mathbb Z}/4$ are homotopy equivalent. In this case, we show that there are four homeomorphism types, and propose a candidate for a smooth example which is not homeomorphic to the geometric quotient. If $\\pi\\cong {\\mathbb Z}/2 \\times {\\mathbb Z}/2$, we show that there are three homotopy types (and between 6 and 24 homeomorphism types).",
  "revisions": [
    {
      "version": "v1",
      "updated": "2017-12-13T00:03:05.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "57N13"
    ],
    "keywords": [
      "homeomorphism types",
      "euler characteristic",
      "smooth example",
      "homotopy types",
      "homotopy equivalent"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 18,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}