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 language | English (US) |
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Pages (from-to) | 95-110 |
Number of pages | 16 |
Journal | Journal of the Mathematical Society of Japan |
Volume | 70 |
Issue number | 1 |
DOIs | |
State | Published - 2018 |
Keywords
- Fibered knot
- L-space knot
- Montesinos knot
ASJC Scopus subject areas
- Mathematics(all)