Slopes for Pretzel Knots
Geometric Topology
2016-02-16 v1
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.
Keywords
Cite
@article{arxiv.1602.04546,
title = {Slopes for Pretzel Knots},
author = {Christine Ruey Shan Lee and Roland van der Veen},
journal= {arXiv preprint arXiv:1602.04546},
year = {2016}
}