{
  "id": "math/9905102",
  "version": "v1",
  "published": "1999-05-18T18:42:22.000Z",
  "updated": "1999-05-18T18:42:22.000Z",
  "title": "A Geometric Interpretation of the χ-{y} Genus on Hyper-Kahler Manifolds",
  "authors": [
    "George Thompson"
  ],
  "doi": "10.1007/s002200000230",
  "categories": [
    "math.AG",
    "hep-th",
    "math-ph",
    "math.DG",
    "math.MP"
  ],
  "abstract": "The group SL(2) acts on the space of cohomology groups of any hyper-Kahler manifold X. The \\chi_{y} genus of a hyper-Kahler X is shown to have a geometric interpretation as the super trace of an element of SL(2). As a by product one learns that the generalized Casson invariant for a mapping torus is essentially the \\chi_{y} genus.",
  "revisions": [
    {
      "version": "v1",
      "updated": "1999-05-18T18:42:22.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "geometric interpretation",
      "hyper-kahler manifold",
      "cohomology groups",
      "group sl",
      "super trace"
    ],
    "tags": [
      "journal article"
    ],
    "publication": {
      "publisher": "Springer",
      "journal": "Communications in Mathematical Physics",
      "year": 2000,
      "volume": 212,
      "number": 3,
      "pages": 649
    },
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2000CMaPh.212..649T"
    }
  }
}