{
  "id": "1605.01016",
  "version": "v1",
  "published": "2016-05-03T18:38:02.000Z",
  "updated": "2016-05-03T18:38:02.000Z",
  "title": "Klein-four connections and the Casson invariant for non-trivial admissible $U(2)$ bundles",
  "authors": [
    "Christopher Scaduto",
    "Matthew Stoffregen"
  ],
  "comment": "17 pages, 2 figures",
  "categories": [
    "math.GT"
  ],
  "abstract": "Given a rank 2 hermitian bundle over a 3-manifold that is non-trivial admissible in the sense of Floer, one defines its Casson invariant as half the signed count of its projectively flat connections, suitably perturbed. We show that the 2-divisibility of this integer invariant is controlled in part by a formula involving the mod 2 cohomology ring of the 3-manifold. This formula counts flat connections on the induced adjoint bundle with Klein-four holonomy.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2016-05-03T18:38:02.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "57M27"
    ],
    "keywords": [
      "casson invariant",
      "non-trivial admissible",
      "klein-four connections",
      "formula counts flat connections",
      "klein-four holonomy"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 17,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}