The Slope Conjecture for Montesinos knots
Stavros Garoufalidis, Christine Ruey Shan Lee, and Roland van der Veen
TL;DR
This paper proves the Slope Conjecture for Montesinos knots by linking the degree of their colored Jones polynomial to boundary slopes of incompressible surfaces, using the Hatcher-Oertel algorithm.
Contribution
It establishes the Slope Conjecture for Montesinos knots and connects polynomial parameters with incompressible surface descriptions.
Findings
Proves the Slope Conjecture for Montesinos knots.
Matches polynomial parameters with incompressible surface parameters.
Uses the Hatcher-Oertel algorithm for the correspondence.
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.
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