{
  "id": "1810.10355",
  "version": "v1",
  "published": "2018-10-22T21:15:39.000Z",
  "updated": "2018-10-22T21:15:39.000Z",
  "title": "Heegaard Floer homology for manifolds with torus boundary: properties and examples",
  "authors": [
    "Jonathan Hanselman",
    "Jacob Rasmussen",
    "Liam Watson"
  ],
  "comment": "73 pages, 66 figures. arXiv admin note: text overlap with arXiv:1604.03466",
  "categories": [
    "math.GT"
  ],
  "abstract": "This is a companion paper to earlier work of the authors, which interprets the Heegaard Floer homology for a manifold with torus boundary in terms of immersed curves in a punctured torus. We prove a variety of properties of this invariant, paying particular attention to its relation to knot Floer homology, the Thurston norm, and the Turaev torsion. We also give a geometric description of the gradings package from bordered Heegaard Floer homology and establish a symmetry under spin$^c$ conjugation; this symmetry gives rise to genus one mutation invariance in Heegaard Floer homology for closed three-manifolds. Finally, we include more speculative discussions on relationships with Seiberg-Witten theory, Khovanov homology, and $HF^\\pm$. Many examples are included.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2018-10-22T21:15:39.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "torus boundary",
      "properties",
      "bordered heegaard floer homology",
      "knot floer homology",
      "earlier work"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 73,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}