{
  "id": "0810.0687",
  "version": "v5",
  "published": "2008-10-03T18:27:35.000Z",
  "updated": "2014-07-26T06:12:07.000Z",
  "title": "Bordered Heegaard Floer homology: Invariance and pairing",
  "authors": [
    "Robert Lipshitz",
    "Peter Ozsvath",
    "Dylan Thurston"
  ],
  "comment": "277 pages, 59 figures; v5: further corrections and improvements",
  "categories": [
    "math.GT",
    "math.SG"
  ],
  "abstract": "We construct Heegaard Floer theory for 3-manifolds with connected boundary. The theory associates to an oriented, parametrized two-manifold a differential graded algebra. For a three-manifold with parametrized boundary, the invariant comes in two different versions, one of which (type D) is a module over the algebra and the other of which (type A) is an A-infinity module. Both are well-defined up to chain homotopy equivalence. For a decomposition of a 3-manifold into two pieces, the A-infinity tensor product of the type D module of one piece and the type A module from the other piece is HF^ of the glued manifold. As a special case of the construction, we specialize to the case of three-manifolds with torus boundary. This case can be used to give another proof of the surgery exact triangle for HF^. We relate the bordered Floer homology of a three-manifold with torus boundary with the knot Floer homology of a filling.",
  "revisions": [
    {
      "version": "v5",
      "updated": "2014-07-26T06:12:07.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "53D40"
    ],
    "keywords": [
      "bordered heegaard floer homology",
      "invariance",
      "torus boundary",
      "construct heegaard floer theory",
      "surgery exact triangle"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 277,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2008arXiv0810.0687L"
    }
  }
}