{
  "id": "1708.07879",
  "version": "v1",
  "published": "2017-08-25T20:55:18.000Z",
  "updated": "2017-08-25T20:55:18.000Z",
  "title": "$\\mathrm{Pin}(2)$-Monopole Floer homology and the Rokhlin invariant",
  "authors": [
    "Francesco Lin"
  ],
  "comment": "17 pages, 2 figures, comments are welcome!",
  "categories": [
    "math.GT"
  ],
  "abstract": "We show that the bar version of the $\\mathrm{Pin}(2)$-monopole Floer homology of a three-manifold $Y$ equipped with a self-conjugate spin$^c$ structure $\\mathfrak{s}$ is determined by the triple cup product of $Y$ together with the Rokhlin invariants of the spin structures inducing $\\mathfrak{s}$. This is a manifestation of mod $2$ index theory, and can be interpreted as a three-dimensional counterpart of Atiyah's classic results regarding spin structures on Riemann surfaces.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2017-08-25T20:55:18.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "monopole floer homology",
      "rokhlin invariant",
      "atiyahs classic results regarding spin",
      "classic results regarding spin structures",
      "triple cup product"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 17,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}