New York Journal of Mathematics
Volume 22 (2016) 1339-1364


Christine Ruey Shan Lee and Roland van der Veen

Slopes for pretzel knots

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Published: November 11, 2016
Keywords: Colored Jones polynomial, Hatcher-Oertel, boundary slopes, knot, link, Jones polynomial, Jones slope, Montesinos knots, incompressible surfaces, slope, state sums
Subject: Primary 57M27, Secondary 57M25

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 a knot determine a boundary slope as predicted by the Slope Conjecture, and that the linear terms in the degrees correspond to the Euler characteristic of an essential surface.


Lee was supported by NSF grant MSPRF-DMS 1502860. Van der Veen was supported by the Netherlands foundation for scientific research (NWO)

Author information

Christine Ruey Shan Lee:
Department of Mathematics, University of Texas, Austin TX 78712

Roland van der Veen:
Mathematisch Instituut, Leiden University, Leiden, Netherlands