Cancellations in the degree of the colored Jones polynomial
Christine Ruey Shan Lee, Roland van der Veen
TL;DR
This paper presents an alternative expansion for the colored Jones polynomial of pretzel links, enabling the determination of degrees for a new family of 3-tangle pretzel knots, thus advancing understanding in quantum topology.
Contribution
It introduces a novel expansion method for the colored Jones polynomial that recovers known degree formulas and applies it to new pretzel knot families.
Findings
Recovered degree formula for pretzel links
Determined degrees for new 3-tangle pretzel knots
Enhanced computational techniques for colored Jones polynomials
Abstract
We give an alternate expansion of the colored Jones polynomial of pretzel links which recovers the degree formula in arXiv:1807.00957. As an application, we determine the degrees of the colored Jones polynomials of a new family of 3-tangle pretzel knots.
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