{
  "id": "1405.6487",
  "version": "v3",
  "published": "2014-05-26T07:39:32.000Z",
  "updated": "2015-09-17T02:22:58.000Z",
  "title": "L-space surgery and twisting operation",
  "authors": [
    "Kimihiko Motegi"
  ],
  "comment": "The final version, accepted for publication by Algebr. Geom. Topol",
  "categories": [
    "math.GT"
  ],
  "abstract": "A knot in the 3-sphere is called an L-space knot if it admits a nontrivial Dehn surgery yielding an L-space, i.e. a rational homology 3-sphere with the smallest possible Heegaard Floer homology. Given a knot K, take an unknotted circle c and twist K n times along c to obtain a twist family { K_n }. We give a sufficient condition for { K_n } to contain infinitely many L-space knots. As an application we show that for each torus knot and each hyperbolic Berge knot K, we can take c so that the twist family { K_n } contains infinitely many hyperbolic L-space knots. We also demonstrate that there is a twist family of hyperbolic L-space knots each member of which has tunnel number greater than one.",
  "revisions": [
    {
      "version": "v2",
      "updated": "2014-07-31T04:32:36.000Z",
      "abstract": "A knot in the 3-sphere is called an L-space knot if it admits a nontrivial Dehn surgery yielding an L-space, which is a generalization of a lens space from the algebraic viewpoint of Heegaard Floer homology. Given an L-space knot K, can we obtain an infinite family of L-space knots by twistings K along a suitably chosen unknotted circle? We consider this question in the case where K admits a Seifert surgery, and give a sufficient condition on such an unknotted circle. If K is a torus knot, then we have an unknotted circle c such that twistings along c produce an infinite family of hyperbolic, L-space knots. In particular, for the trivial knot we can take infinitely many such unknotted circles. We also demonstrate that there are infinitely many hyperbolic, L-space knots with tunnel number greater than one, each of which arises from a trefoil knot by alternate twistings along two unknotted circles.",
      "comment": "Some results refined, exposition improved",
      "journal": null,
      "doi": null
    },
    {
      "version": "v3",
      "updated": "2015-09-17T02:22:58.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "57M25",
      "57M27"
    ],
    "keywords": [
      "l-space knot",
      "unknotted circle",
      "l-space surgery",
      "twisting operation",
      "tunnel number greater"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2014arXiv1405.6487M"
    }
  }
}