Slopes for Pretzel Knots

Abstract

Using the Hatcher-Oertel algorithm for finding boundary slopes of Montesinos knots, we prove the Slope Conjecture and the Strong Slope Conjecture for a family of 3-tangle pretzel knots. More precisely, we prove that the maximal degrees of the colored Jones polynomial of such knots determine a boundary slope as predicted by the Slope Conjecture, and that the linear term in the degrees correspond to the Euler characteristic of an essential surface.