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Christine Ruey Shan Lee and Roland van der Veen
Slopes for pretzel knots view print
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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 |
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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 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.
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| Acknowledgements
Lee was supported by NSF grant MSPRF-DMS 1502860. Van der Veen was supported by the Netherlands foundation for scientific research (NWO)
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| Author information
Christine Ruey Shan Lee:
Department of Mathematics, University of Texas, Austin TX 78712
clee@math.utexas.edu
Roland van der Veen:
Mathematisch Instituut, Leiden University, Leiden, Netherlands
r.i.van.der.veen@math.leidenuniv.nl
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