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) |
|---|---|
| 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 - Jan 1 2018 |
Keywords
- Fibered knot
- L-space knot
- Montesinos knot
ASJC Scopus subject areas
- Mathematics(all)
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Baker, K., & Moore, A. H. (2018). Montesinos knots, hopf plumbings, and L-space surgeries. Journal of the Mathematical Society of Japan, 70(1), 95-110. https://doi.org/10.2969/jmsj/07017484