{
  "id": "math/0302131",
  "version": "v2",
  "published": "2003-02-11T20:34:37.000Z",
  "updated": "2003-06-09T00:32:47.000Z",
  "title": "Rohlin's invariant and gauge theory, I. Homology 3-tori",
  "authors": [
    "Daniel Ruberman",
    "Nikolai Saveliev"
  ],
  "comment": "Changed title to fit with succeeding papers in series. Added reference to Turaev's work",
  "journal": "Comm. Math. Helv., 79 (2004), no. 3, 618--646.",
  "categories": [
    "math.GT"
  ],
  "abstract": "This is the first in a series of papers exploring the relationship between the Rohlin invariant and gauge theory. We discuss the Casson-type invariant of a 3-manifold with the integral homology of a torus, given by counting projectively flat connections. We show that its mod 2 evaluation is given by the triple cup product in cohomology, and so it coincides with a sum of Rohlin invariants. Our counting argument makes use of a natural action of the first cohomology on the moduli space of projectively flat connections; along the way we construct perturbations that are equivariant with respect to this action. Combined with the Floer exact triangle, this gives a purely gauge-theoretic proof that Casson's homology sphere invariant reduces mod 2 to the Rohlin invariant.",
  "revisions": [
    {
      "version": "v2",
      "updated": "2003-06-09T00:32:47.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "57N10"
    ],
    "keywords": [
      "gauge theory",
      "rohlins invariant",
      "rohlin invariant",
      "homology sphere invariant reduces mod",
      "cassons homology sphere invariant reduces"
    ],
    "tags": [
      "journal article"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "inspire": 622637,
      "adsabs": "2003math......2131R"
    }
  }
}