Slopes for Pretzel Knots

Christine Ruey Shan Lee; Roland van der Veen

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arXiv · 1602.04546

Slopes for Pretzel Knots

Christine Ruey Shan Lee·Roland van der Veen

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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.

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Christine Ruey Shan Lee, Roland van der Veen. 2016-02-15. Slopes for Pretzel Knots. https://arxiv.org/abs/1602.04546

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