{
  "id": "math/0403335",
  "version": "v2",
  "published": "2004-03-20T21:39:07.000Z",
  "updated": "2005-03-13T23:48:26.000Z",
  "title": "Elliptic operators on manifolds with singularities and K-homology",
  "authors": [
    "A. Savin"
  ],
  "comment": "revised version; 25 pages; section with applications expanded",
  "journal": "K-Theory, Vol. 34, No. 1. (January 2005), pp. 71-98",
  "doi": "10.1007/s10977-005-1515-1",
  "categories": [
    "math.OA",
    "math.AP",
    "math.KT"
  ],
  "abstract": "It is well known that elliptic operators on a smooth compact manifold are classified by K-homology. We prove that a similar classification is also valid for manifolds with simplest singularities: isolated conical points and fibered boundary. The main ingredients of the proof of these results are: an analog of the Atiyah-Singer difference construction in the noncommutative case and an analog of Poincare isomorphism in K-theory for our singular manifolds. As applications we give a formula in topological terms for the obstruction to Fredholm problems on manifolds with singularities and a formula for K-groups of algebras of pseudodifferential operators.",
  "revisions": [
    {
      "version": "v2",
      "updated": "2005-03-13T23:48:26.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "58J05",
      "19K33",
      "35S35",
      "47L15"
    ],
    "keywords": [
      "elliptic operators",
      "k-homology",
      "smooth compact manifold",
      "atiyah-singer difference construction",
      "fredholm problems"
    ],
    "tags": [
      "journal article"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 25,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2004math......3335S"
    }
  }
}