On the degree of the colored Jones polynomial

Efstratia Kalfagianni; Christine Ruey Shan Lee

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arXiv · 1311.6059

On the degree of the colored Jones polynomial

Efstratia Kalfagianni·Christine Ruey Shan Lee

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Abstract

The extreme degrees of the colored Jones polynomial of any link are bounded in terms of concrete data from any link diagram. It is known that these bounds are sharp for semi-adequate diagrams. One of the goals of this paper is to show the converse; if the bounds are sharp then the diagram is semi-adequate. As a result, we use colored Jones link polynomials to extract an invariant that detects semi-adequate links and discuss some applications.

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Efstratia Kalfagianni, Christine Ruey Shan Lee. 2014-06-17. On the degree of the colored Jones polynomial. https://arxiv.org/abs/1311.6059

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