Montesinos knots, Hopf plumbings, and L-space surgeries

2014/04/30 by Baker, Kenneth L., Moore, Allison H. · 1 citation
#FOS: Mathematics #Geometric Topology (math.GT)

paper · doi:10.48550/arxiv.1404.7585

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.

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• SL₂(\mathbb R)-representations and left-orderable surgeries of (-2, 3, 2n+1)-pretzel knots

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