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.

References in corpus (3)

• On the characteristic and deformation varieties of a knot
• Slopes and colored Jones polynomials of adequate knots
• Quadratic integer programming and the slope conjecture

Cited by in corpus (5)

• The slope conjecture for graph knots
• Jones slopes and coarse volume of near-alternating links
• The strong slope conjecture for cablings and connected sums
• The Slope Conjecture for a Family of Montesinos Knots
• Geometric estimates from spanning surfaces