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The slope conjecture for Montesinos knots

International Center for Mathematics, Department of Mathematics, Southern University of Science and Technology Shenzhen, P. R. China

E-mail Address: stavros@mpim-bonn.mpg.de

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Christine Ruey Shan Lee

http://orcid.org/0000-0002-9572-7514

University of South Alabama, 411 University Boulevard North, Mobile, AL 36608, USA

E-mail Address: crslee@southalabama.edu

Corresponding author.

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, and

Roland van der Veen

University of Groningen, Bernoulli Institute, P. O. Box 407, 9700 AK Groningen, The Netherlands

E-mail Address: r.i.van.der.veen@rug.nl

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https://doi.org/10.1142/S0129167X20500561Cited by:3 (Source: Crossref)

Abstract

The slope conjecture relates the degree of the colored Jones polynomial of a knot to boundary slopes of essential surfaces. We develop a general approach that matches a state-sum formula for the colored Jones polynomial with the parameters that describe surfaces in the complement. We apply this to Montesinos knots proving the slope conjecture for Montesinos knots, with some restrictions.

Keywords:

AMSC: 57N10, 57M25

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