## Abstract

Let D be a diagram of an alternating knot with unknotting number one. The branched double cover of S3 branched over D is an L-space obtained by half integral surgery on a knot KD. We denote the set of all such knots KD by D. We characterize when KD 2 D is a torus knot, a satellite knot or a hyperbolic knot. In a different direction, we show that for a given n > 0, there are only finitely many L-space knots in D with genus less than n.

Original language | English |
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Pages (from-to) | 518-540 |

Number of pages | 23 |

Journal | New York Journal of Mathematics |

Volume | 25 |

Early online date | 20 Jun 2019 |

Publication status | E-pub ahead of print - 20 Jun 2019 |