Stability properties of the colored Jones polynomial

Lee, Christine Ruey Shan

doi:10.48550/arxiv.1409.4457

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Introduction2

Jones Surfaces Of Adequate Knots1

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2018

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Cited by 2 publications

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“…Inequalities 7 and 8, that generalize and strengthen results of [18], have been more recently established by Lee. See [22,Theorem 2.4] or [21]. Theorem 3.2.…”

Section: Jones Surfaces Of Adequate Knotsmentioning

confidence: 99%

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A Jones slopes characterization of adequate knots

Kalfagianni¹

2018

Indiana Univ. Math. J.

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We establish a characterization of adequate knots in terms of the degree of their colored Jones polynomial. We show that, assuming the Strong Slope conjecture, our characterization can be reformulated in terms of "Jones slopes" of knots and the essential surfaces that realize the slopes. For alternating knots the reformulated characterization follows by recent work of J. Greene and J. Howie.2010 Mathematics Classification: 57N10, 57M25.

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“…Inequalities 7 and 8, that generalize and strengthen results of [18], have been more recently established by Lee. See [22,Theorem 2.4] or [21]. Theorem 3.2.…”

Section: Jones Surfaces Of Adequate Knotsmentioning

confidence: 99%

“…Some ingredients for the proof of Theorem 1.1 are a result of Lee [22,21] on upper bounds on the degree of the colored Jones polynomial and a result of Abe [1] on the Turaev genus of adequate knots.…”

Section: Introductionmentioning

confidence: 99%

A Jones slopes characterization of adequate knots

Kalfagianni¹

2018

Indiana Univ. Math. J.

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“…This conjecture was proven by Armond [1] and independently by Garoufalidis and Lê [11] where higher stability were also shown. This work was extended to quantum spin networks in [12] and all links in [20,21]. Dasbach and Lin showed that the head and tail of alternating links contain geometric information that can be used as bounds for the hyperbolic volume of a non-torus alternating links [7].…”

Section: Introductionmentioning

confidence: 99%