{
  "id": "math/0404162",
  "version": "v3",
  "published": "2004-04-07T12:18:28.000Z",
  "updated": "2005-10-28T11:34:57.000Z",
  "title": "Rohlin's invariant and gauge theory III. Homology 4--tori",
  "authors": [
    "Daniel Ruberman",
    "Nikolai Saveliev"
  ],
  "comment": "Published by Geometry and Topology at http://www.maths.warwick.ac.uk/gt/GTVol9/paper47.abs.html",
  "journal": "Geom. Topol. 9(2005) 2079-2127",
  "categories": [
    "math.GT"
  ],
  "abstract": "This is the third in our series of papers relating gauge theoretic invariants of certain 4-manifolds with invariants of 3-manifolds derived from Rohlin's theorem. Such relations are well-known in dimension three, starting with Casson's integral lift of the Rohlin invariant of a homology sphere. We consider two invariants of a spin 4-manifold that has the integral homology of a 4-torus. The first is a degree zero Donaldson invariant, counting flat connections on a certain SO(3)-bundle. The second, which depends on the choice of a 1-dimensional cohomology class, is a combination of Rohlin invariants of a 3-manifold carrying the dual homology class. We prove that these invariants, suitably normalized, agree modulo 2, by showing that they coincide with the quadruple cup product of 1-dimensional cohomology classes.",
  "revisions": [
    {
      "version": "v3",
      "updated": "2005-10-28T11:34:57.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "57R57",
      "57R58"
    ],
    "keywords": [
      "rohlins invariant",
      "gauge theory",
      "papers relating gauge theoretic invariants",
      "degree zero donaldson invariant",
      "rohlin invariant"
    ],
    "tags": [
      "journal article"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2004math......4162R"
    }
  }
}