The Khovanov width of twisted links and closed 3-braids

Lowrance, Adam M.

doi:10.4171/cmh/238

Cited by 16 publications

(13 citation statements)

References 19 publications

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“…Remark 3.1. Since the 3-braids of Theorem 3.1 (which satisfy the assumptions of Lemma 2.1) are generic, then Proposition 4.15 of [14] implies, with the assumption that k = 0, that…”

Section: Volume Bounds In Terms Of the Schreier Normal Formmentioning

confidence: 99%

Semi-adequate closed braids and volume

Giambrone¹

2016

Topology and its Applications

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In this paper, we show that the volumes for a family of A-adequate closed braids can be bounded above and below in terms of the twist number, the number of braid strings, and a quantity that can be read from the combinatorics of a given closed braid diagram. We also show that the volumes for many of these closed braids can be bounded in terms of a single stable coefficient of the colored Jones polynomial, thus showing that this collection of closed braids satisfies a Coarse Volume Conjecture. By expanding to a wider family of closed braids, we also obtain volume bounds in terms of the number of positive and negative twist regions in a given closed braid diagram. Furthermore, for a family of A-adequate closed 3-braids, we show that the volumes can be bounded in terms of the parameter s from the Schreier normal form of the 3-braid. Finally we show that, for the same family of A-adequate closed 3-braids, the parameters k and s from the Schreier normal form can actually be read off of the original 3-braid word.

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“…Remark 3.1. Since the 3-braids of Theorem 3.1 (which satisfy the assumptions of Lemma 2.1) are generic, then Proposition 4.15 of [14] implies, with the assumption that k = 0, that…”

Section: Volume Bounds In Terms Of the Schreier Normal Formmentioning

confidence: 99%

Semi-adequate closed braids and volume

Giambrone¹

2016

Topology and its Applications

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“…Lowrance [22] and Watson [36] have proved that the width of Khovanov homology remains unchanged after replacing a crossing in a link diagram with an alternating rational tangle, provided the crossing satisfies certain conditions. Using Corollary 4.6, this generates many families of knots with unbounded Turaev genus.…”

Section: Turaev Genus and Khovanov Homologymentioning

confidence: 99%

A Survey on the Turaev Genus of Knots

Champanerkar

Kofman

2014

Acta Math Vietnam

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“…Using Inequality 3.1 and work of Stošić [Sto09] and Turner [Tur08], the author [Low11] computes the Turaev genus of the (3, q)-torus knots. Abe and Kishimoto [AK10] independently compute the Turaev genus of the (3, q)-torus knots and also compute their dealternating numbers.…”

Section: Proof Proposition 44 Implies That Ifmentioning

confidence: 99%