{
  "id": "1207.3066",
  "version": "v4",
  "published": "2012-07-12T19:09:43.000Z",
  "updated": "2014-09-16T18:07:16.000Z",
  "title": "Morse theory for manifolds with boundary",
  "authors": [
    "Maciej Borodzik",
    "András Némethi",
    "Andrew Ranicki"
  ],
  "comment": "v4. 38 pages, 20 figures, minor revision, updated references to Braess, Jankowski--Rubinstein and Hajduk",
  "categories": [
    "math.GT",
    "math.AT"
  ],
  "abstract": "We develop Morse theory for manifolds with boundary. Besides standard and expected facts like the handle cancellation theorem and the Morse lemma for manifolds with boundary, we prove that, under a topological assumption, a critical point in the interior of a Morse function can be moved to the boundary, where it splits into a pair of boundary critical points. As an application, we prove that every cobordism of manifolds with boundary splits as a union of left product cobordisms and right product cobordisms.",
  "revisions": [
    {
      "version": "v3",
      "updated": "2012-11-27T01:41:42.000Z",
      "comment": "34 pages, 18 figures, updated bibliography",
      "journal": null,
      "doi": null
    },
    {
      "version": "v4",
      "updated": "2014-09-16T18:07:16.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "57R19",
      "58E05",
      "58A05"
    ],
    "keywords": [
      "morse theory",
      "left product cobordisms",
      "right product cobordisms",
      "handle cancellation theorem",
      "morse function"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 38,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2012arXiv1207.3066B"
    }
  }
}