{
  "id": "1403.6215",
  "version": "v3",
  "published": "2014-03-25T02:51:54.000Z",
  "updated": "2016-11-27T00:48:51.000Z",
  "title": "Explicit Koszul-dualizing bimodules in bordered Heegaard Floer homology",
  "authors": [
    "Bohua Zhan"
  ],
  "comment": "50 pages",
  "journal": "Algebr. Geom. Topol. 16 (2016) 231-266",
  "doi": "10.2140/agt.2016.16.231",
  "categories": [
    "math.GT"
  ],
  "abstract": "We give a combinatorial proof of the quasi-invertibility of $\\widehat{CFDD}(\\mathbb{I}_\\mathcal{Z})$ in bordered Heegaard Floer homology, which implies a Koszul self-duality on the dg-algebra $\\mathcal{A}(\\mathcal{Z})$, for each pointed matched circle $\\mathcal{Z}$. This is done by giving an explicit description of a rank 1 model for $\\widehat{CFAA}(\\mathbb{I}_\\mathcal{Z})$, the quasi-inverse of $\\widehat{CFDD}(\\mathbb{I}_\\mathcal{Z})$. This description is obtained by applying homological perturbation theory to a larger, previously known model of $\\widehat{CFAA}(\\mathbb{I}_\\mathcal{Z})$.",
  "revisions": [
    {
      "version": "v2",
      "updated": "2014-05-28T01:02:26.000Z",
      "comment": "49 pages",
      "journal": null,
      "doi": null
    },
    {
      "version": "v3",
      "updated": "2016-11-27T00:48:51.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "57R58",
      "57R56"
    ],
    "keywords": [
      "bordered heegaard floer homology",
      "explicit koszul-dualizing bimodules",
      "combinatorial proof",
      "koszul self-duality",
      "applying homological perturbation theory"
    ],
    "tags": [
      "journal article"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 50,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2014arXiv1403.6215Z"
    }
  }
}