{
  "id": "1512.03939",
  "version": "v1",
  "published": "2015-12-12T17:33:34.000Z",
  "updated": "2015-12-12T17:33:34.000Z",
  "title": "Cobordism Invariance of the Index of Callias-Type Operators",
  "authors": [
    "Maxim Braverman",
    "Pengshuai Shi"
  ],
  "comment": "17 pages",
  "categories": [
    "math.DG"
  ],
  "abstract": "We introduce a notion of cobordism of Callias-type operators over complete Riemannian manifolds and prove that the index is preserved by such a cobordism. As an application we prove a gluing formula for Callias-type index. In particular, a usual index of an elliptic operator on a compact manifold can be computed as a sum of indexes of Callias-type operators on two non-compact, but topologically simpler manifolds. As another application we give a new proof of the relative index theorem for Callias-type operators, which also leads to a new proof of the Callias index theorem.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2015-12-12T17:33:34.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "callias-type operators",
      "cobordism invariance",
      "callias index theorem",
      "complete riemannian manifolds",
      "elliptic operator"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 17,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}