{
  "id": "1411.0353",
  "version": "v1",
  "published": "2014-11-03T03:52:07.000Z",
  "updated": "2014-11-03T03:52:07.000Z",
  "title": "Detection of knots and a cabling formula for A-polynomials",
  "authors": [
    "Yi Ni",
    "Xingru Zhang"
  ],
  "comment": "29 pages, 5 figures",
  "categories": [
    "math.GT"
  ],
  "abstract": "We say that a given knot $J\\subset S^3$ is detected by its knot Floer homology and $A$-polynomial if whenever a knot $K\\subset S^3$ has the same knot Floer homology and the same $A$-polynomial as $J$, then $K=J$. In this paper we show that every torus knot $T(p,q)$ is detected by its knot Floer homology and $A$-polynomial. We also give a one-parameter family of infinitely many hyperbolic knots in $S^3$ each of which is detected by its knot Floer homology and $A$-polynomial. In addition we give a cabling formula for the A-polynomials of cabled knots in $S^3$, which is of independent interest. In particular we give explicitly the A-polynomials of iterated torus knots.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2014-11-03T03:52:07.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "57M25",
      "57M27"
    ],
    "keywords": [
      "knot floer homology",
      "cabling formula",
      "a-polynomials",
      "iterated torus knots",
      "independent interest"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 29,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2014arXiv1411.0353N"
    }
  }
}