{
  "id": "math/0306188",
  "version": "v2",
  "published": "2003-06-11T15:36:45.000Z",
  "updated": "2004-02-12T10:10:55.000Z",
  "title": "Rohlin's invariant and gauge theory II. Mapping tori",
  "authors": [
    "Daniel Ruberman",
    "Nikolai Saveliev"
  ],
  "comment": "Published by Geometry and Topology at http://www.maths.warwick.ac.uk/gt/GTVol8/paper2.abs.html",
  "journal": "Geom.Topol. 8 (2004) 35-76",
  "categories": [
    "math.GT",
    "math.DG"
  ],
  "abstract": "This is the second in a series of papers studying the relationship between Rohlin's theorem and gauge theory. We discuss an invariant of a homology S^1 cross S^3 defined by Furuta and Ohta as an analogue of Casson's invariant for homology 3-spheres. Our main result is a calculation of the Furuta-Ohta invariant for the mapping torus of a finite-order diffeomorphism of a homology sphere. The answer is the equivariant Casson invariant (Collin-Saveliev 2001) if the action has fixed points, and a version of the Boyer-Nicas (1990) invariant if the action is free. We deduce, for finite-order mapping tori, the conjecture of Furuta and Ohta that their invariant reduces mod 2 to the Rohlin invariant of a manifold carrying a generator of the third homology group. Under some transversality assumptions, we show that the Furuta-Ohta invariant coincides with the Lefschetz number of the action on Floer homology. Comparing our two answers yields an example of a diffeomorphism acting trivially on the representation variety but non-trivially on Floer homology.",
  "revisions": [
    {
      "version": "v2",
      "updated": "2004-02-12T10:10:55.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "57R57",
      "57R58"
    ],
    "keywords": [
      "mapping torus",
      "gauge theory",
      "rohlins invariant",
      "floer homology",
      "third homology group"
    ],
    "tags": [
      "journal article"
    ],
    "publication": {
      "doi": "10.2140/gt.2004.8.35"
    },
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "inspire": 620934
    }
  }
}