The Vol-Det Conjecture for highly twisted alternating links

Andrei Egorov; Andrei Vesnin

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arXiv · 2411.11711

The Vol-Det Conjecture for highly twisted alternating links

Andrei Egorov·Andrei Vesnin

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Abstract

The Vol-Det Conjecture, formulated by Champanerkar, Kofman and Purcell, states that there exists a specific inequality connecting the hyperbolic volume of an alternating link and its determinant. Among the classes of links for which this conjecture holds are all alternating hyperbolic knots with at most 16 crossings, 2-bridge links, and links that are closures of 3-strand braids. In the present paper, Burton's bound on the number of crossings for which the Vol-Det Conjecture holds is improved for links with more than eight twists. In addition, Stoimenow's inequalities between hyperbolic volumes and determinants are improved for alternating and alternating arborescent links with more than eight twists.

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Andrei Egorov, Andrei Vesnin. 2024-11-18. The Vol-Det Conjecture for highly twisted alternating links. https://arxiv.org/abs/2411.11711

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