Twist families of L-space knots, their genera, and Seifert surgeries

Kenneth L. Baker, Kimihiko Motegi

Research output: Contribution to journalArticlepeer-review


Conjecturally, there are only finitely many Heegaard Floer L-space knots in S3 of a given genus. We examine this conjecture for twist families of knots {Kn} obtained by twisting a knot K in S3 along an unknot c in terms of the linking number ω between K and c. We establish the conjecture in the case of |ω| ≠ 1, prove that {Kn} contains at most three L-space knots if ω = 0, and address the case where |ω| = 1 under an additional hypothesis about Seifert surgeries. To that end, we characterize a twisting circle c for which {(Kn, rn)} 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.

Original languageEnglish (US)
Pages (from-to)743-790
Number of pages48
JournalCommunications in Analysis and Geometry
Issue number4
StatePublished - 2019

ASJC Scopus subject areas

  • Analysis
  • Statistics and Probability
  • Geometry and Topology
  • Statistics, Probability and Uncertainty


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