{
  "id": "0707.2321",
  "version": "v1",
  "published": "2007-07-16T14:03:01.000Z",
  "updated": "2007-07-16T14:03:01.000Z",
  "title": "Chern-Simons classes of flat connections on supermanifolds",
  "authors": [
    "JN Iyer",
    "Un Iyer"
  ],
  "categories": [
    "math.AG",
    "math-ph",
    "math.MP"
  ],
  "abstract": "In this note we define Chern-Simons classes of a superconnection $D+L$ on a complex supervector bundle $E$ such that $D$ is flat and preserves the grading, and $L$ is an odd endomorphism of $E$ on a supermanifold. As an application we obtain a definition of Chern-Simons classes of a (not necessarily flat) morphism between flat vector bundles on a smooth manifold. We extend Reznikov's theorem on triviality of these classes when the manifold is a compact K\\\"ahler manifold or a smooth complex quasi--projective variety, in degrees > 1.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2007-07-16T14:03:01.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "53C05",
      "53C07",
      "53C29"
    ],
    "keywords": [
      "flat connections",
      "supermanifold",
      "flat vector bundles",
      "smooth complex quasi-projective variety",
      "complex supervector bundle"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2007arXiv0707.2321I"
    }
  }
}