{
  "id": "1501.00028",
  "version": "v1",
  "published": "2014-12-30T21:57:07.000Z",
  "updated": "2014-12-30T21:57:07.000Z",
  "title": "The pillowcase and traceless representations of knot groups II: a Lagrangian-Floer theory in the pillowcase",
  "authors": [
    "Matthew Hedden",
    "Christopher M. Herald",
    "Paul Kirk"
  ],
  "comment": "66 pages, 25 figures",
  "categories": [
    "math.GT"
  ],
  "abstract": "We define an elementary relatively $\\mathbb Z/4$ graded Lagrangian-Floer chain complex for restricted immersions of compact 1-manifolds into the pillowcase, and apply it to the intersection diagram obtained by taking traceless $SU(2)$ character varieties of 2-tangle decompositions of knots. Calculations for torus knots are explained in terms of pictures in the punctured plane. The relation to the reduced instanton homology of knots is explored.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2014-12-30T21:57:07.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "57M27",
      "57R58",
      "57M25",
      "81T13"
    ],
    "keywords": [
      "pillowcase",
      "knot groups",
      "lagrangian-floer theory",
      "traceless representations",
      "graded lagrangian-floer chain complex"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 66,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "inspire": 1336400,
      "adsabs": "2015arXiv150100028H"
    }
  }
}