{
  "id": "1803.01765",
  "version": "v1",
  "published": "2018-03-05T16:42:35.000Z",
  "updated": "2018-03-05T16:42:35.000Z",
  "title": "Simply-connected, spineless 4-manifolds",
  "authors": [
    "Adam Simon Levine",
    "Tye Lidman"
  ],
  "comment": "7 pages, 3 figures",
  "categories": [
    "math.GT"
  ],
  "abstract": "We construct infinitely many smooth 4-manifolds which are homotopy equivalent to $S^2$ but do not admit a spine, i.e., a piecewise-linear embedding of $S^2$ which realizes the homotopy equivalence. This is the remaining case in the existence problem for codimension-2 spines in simply-connected manifolds. The obstruction comes from the Heegaard Floer $d$ invariants.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2018-03-05T16:42:35.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "57M27",
      "57Q35"
    ],
    "keywords": [
      "homotopy equivalent",
      "homotopy equivalence",
      "existence problem",
      "obstruction comes",
      "heegaard floer"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 7,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}