{
  "id": "1506.04455",
  "version": "v1",
  "published": "2015-06-15T01:59:25.000Z",
  "updated": "2015-06-15T01:59:25.000Z",
  "title": "Twist families of L-space knots, their genera, and Seifert surgeries",
  "authors": [
    "Kenneth L. Baker",
    "Kimihiko Motegi"
  ],
  "categories": [
    "math.GT"
  ],
  "abstract": "Conjecturally, there are only finitely many Heegaard Floer L-space knots in $S^3$ of a given genus. We examine this conjecture for twist families of knots $\\{K_n\\}$ obtained by twisting a knot $K$ in $S^3$ along an unknot $c$ in terms of the linking number $\\omega$ between $K$ and $c$. We establish the conjecture in case of $|\\omega| \\neq 1$, prove that $\\{K_n\\}$ contains at most three L-space knots if $\\omega = 0$, and address the case where $|\\omega| = 1$ under an additional hypothesis about Seifert surgeries. To that end, we characterize a twisting circle $c$ for which $\\{ (K_n, r_n) \\}$ contains at least ten Seifert surgeries. We also pose a few questions about the nature of twist families of L-space knots, their expressions as closures of positive (or negative) braids, and their wrapping about the twisting circle.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2015-06-15T01:59:25.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "57M25",
      "57M27"
    ],
    "keywords": [
      "seifert surgeries",
      "twist families",
      "heegaard floer l-space knots",
      "twisting circle",
      "conjecture"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2015arXiv150604455B"
    }
  }
}