{
  "id": "math/0612316",
  "version": "v2",
  "published": "2006-12-12T15:38:16.000Z",
  "updated": "2007-10-12T00:53:50.000Z",
  "title": "Morse-Bott homology",
  "authors": [
    "Augustin Banyaga",
    "David E. Hurtubise"
  ],
  "comment": "53 pages, 4 figures",
  "journal": "Trans. Amer. Math. Soc., 362, no. 8, p. 3997-4043, 2010",
  "categories": [
    "math.AT",
    "math.DS",
    "math.GT"
  ],
  "abstract": "We give a new proof of the Morse Homology Theorem by constructing a chain complex associated to a Morse-Bott-Smale function that reduces to the Morse-Smale-Witten chain complex when the function is Morse-Smale and to the chain complex of smooth singular $N$-cube chains when the function is constant. We show that the homology of the chain complex is independent of the Morse-Bott-Smale function by using compactified moduli spaces of time dependent gradient flow lines to prove a Floer-type continuation theorem.",
  "revisions": [
    {
      "version": "v2",
      "updated": "2007-10-12T00:53:50.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "57R70",
      "58E05",
      "57R58",
      "37D15"
    ],
    "keywords": [
      "morse-bott homology",
      "time dependent gradient flow lines",
      "morse-bott-smale function",
      "floer-type continuation theorem",
      "morse homology theorem"
    ],
    "tags": [
      "journal article"
    ],
    "publication": {
      "publisher": "AMS",
      "journal": "Trans. Amer. Math. Soc."
    },
    "note": {
      "typesetting": "TeX",
      "pages": 53,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2006math.....12316B"
    }
  }
}