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January, 2018 Montesinos knots, Hopf plumbings, and L-space surgeries
Kenneth L. BAKER, Allison H. MOORE
J. Math. Soc. Japan 70(1): 95-110 (January, 2018). DOI: 10.2969/jmsj/07017484


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 $S^3$. 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.


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Kenneth L. BAKER. Allison H. MOORE. "Montesinos knots, Hopf plumbings, and L-space surgeries." J. Math. Soc. Japan 70 (1) 95 - 110, January, 2018.


Published: January, 2018
First available in Project Euclid: 26 January 2018

zbMATH: 06859845
MathSciNet: MR3750269
Digital Object Identifier: 10.2969/jmsj/07017484

Primary: 57M25
Secondary: 57M27

Keywords: fibered knot , L-space knot , Montesinos knot

Rights: Copyright © 2018 Mathematical Society of Japan


Vol.70 • No. 1 • January, 2018
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