The Slope Conjecture for Montesinos knots

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.