Montesinos knots, hopf plumbings, and L-space surgeries

Kenneth Baker, Allison H. Moore

Research output: Contribution to journalArticle

4 Scopus citations

Abstract

Using Hirasawa–Murasugi’s classification of fibered Montesinos knots we classify the L-space Montesinos knots, providing further evidence towards a conjecture of Lidman–Moore that L-space knots have no essential Conway spheres. In the process, we classify the fibered Montesinos knots whose open books support the tight contact structure on S3. We also construct L-space knots with arbitrarily large tunnel number and discuss the question of whether L-space knots admit essential tangle decompositions in the context of satellite operations and tunnel number.

Original languageEnglish (US)
Pages (from-to)95-110
Number of pages16
JournalJournal of the Mathematical Society of Japan
Volume70
Issue number1
DOIs
StatePublished - Jan 1 2018

Keywords

  • Fibered knot
  • L-space knot
  • Montesinos knot

ASJC Scopus subject areas

  • Mathematics(all)

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