{
  "id": "1204.0120",
  "version": "v2",
  "published": "2012-03-31T18:00:59.000Z",
  "updated": "2012-06-01T17:24:54.000Z",
  "title": "The vanishing of L2 harmonic one-forms on based path spaces",
  "authors": [
    "K. D. Elworthy",
    "Y. Yang"
  ],
  "journal": "Journal of Functional Analysis 264 (2013), pp. 1168-1196",
  "doi": "10.1016/j.jfa.2012.12.008",
  "categories": [
    "math.PR"
  ],
  "abstract": "We prove the triviality of the first L2 cohomology class of based path spaces of Riemannian manifolds furnished with Brownian motion measure, and the consequent vanishing of L2 harmonic one-forms. We give explicit formulae for closed and co-closed one-forms expressed as differentials of functions and co-differentials of L2 two-forms, respectively; these are considered as extended Clark-Ocone formulae. A feature of the proof is the use of the temporal structure of path spaces to relate a rough exterior derivative operator on one-forms to the exterior differentiation operator used to construct the de Rham complex and the self-adjoint Laplacian on L2 one-forms. This Laplacian is shown to have a spectral gap.",
  "revisions": [
    {
      "version": "v2",
      "updated": "2012-06-01T17:24:54.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "58J65",
      "60H07",
      "58A12",
      "58A14"
    ],
    "keywords": [
      "l2 harmonic one-forms",
      "path spaces",
      "first l2 cohomology class",
      "brownian motion measure",
      "rough exterior derivative operator"
    ],
    "tags": [
      "journal article"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2012arXiv1204.0120E"
    }
  }
}