{
  "id": "math/0612416",
  "version": "v1",
  "published": "2006-12-14T20:35:42.000Z",
  "updated": "2006-12-14T20:35:42.000Z",
  "title": "An L2 theory for differential forms on path spaces I",
  "authors": [
    "K. D. Elworthy",
    "Xue-Mei Li"
  ],
  "categories": [
    "math.PR"
  ],
  "abstract": "An L2 theory of differential forms is proposed for the Banach manifold of continuous paths on Riemannian manifolds M furnished with its Brownian motion measure. Differentiation must be restricted to certain Hilbert space directions, the H-tangent vectors. To obtain a closed exterior differential operator the relevant spaces of differential forms, the H-forms, are perturbed by the curvature of M. A Hodge decomposition is given for L2 H-one-forms, and the structure of H-two -forms is described. The dual operator d* is analysed in terms of a natural connection on the H-tangent spaces. Malliavin calculus is a basic tool.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2006-12-14T20:35:42.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "differential forms",
      "l2 theory",
      "path spaces",
      "brownian motion measure",
      "hilbert space directions"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2006math.....12416E"
    }
  }
}