The slope conjecture for Montesinos knots

Garoufalidis, Stavros; Lee, Christine Ruey Shan; van der Veen, Roland

doi:10.1142/S0129167X20500561

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The slope conjecture for Montesinos knots

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Lee, Christine Ruey Shan
Max Planck Institute for Mathematics, Max Planck Society;

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https://doi.org/10.1142/S0129167X20500561
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arXiv:1807.00957.pdf
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Citation

Garoufalidis, S., Lee, C. R. S., & van der Veen, R. (2020). The slope conjecture for Montesinos knots. International Journal of Mathematics, 31(7): 2050056. doi:10.1142/S0129167X20500561.

Cite as: https://hdl.handle.net/21.11116/0000-0006-B310-D

Abstract

The Slope Conjecture relates the degree of the colored Jones polynomial of a
knot to boundary slopes of incompressible surfaces. Our aim is to prove the
Slope Conjecture for Montesinos knots, and to match parameters of a
state-formula for the colored Jones polynomial of such knots with the
parameters that describe their corresponding incompressible surfaces via the
Hatcher-Oertel algorithm.