Normal and Jones surfaces of knots

Efstratia Kalfagianni; Christine Ruey Shan Lee

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arXiv · 1702.06466

Normal and Jones surfaces of knots

Efstratia Kalfagianni·Christine Ruey Shan Lee

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Abstract

We describe a normal surface algorithm that decides whether a knot, with known degree of the colored Jones polynomial, satisfies the Strong Slope Conjecture. We also discuss possible simplifications of our algorithm and state related open questions. We establish a relation between the Jones period of a knot and the number of sheets of the surfaces that satisfy the Strong Slope Conjecture (Jones surfaces). We also present numerical and experimental evidence supporting a stronger such relation which we state as an open question.

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Efstratia Kalfagianni, Christine Ruey Shan Lee. 2017-02-21. Normal and Jones surfaces of knots. https://arxiv.org/abs/1702.06466

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