Abstract The Vol–Det Conjecture by Champanerkar, Kofman and Purcell states that there is an inequality relating the hyperbolic volume of an alternating link and its determinant. The classes of links satisfying this conjecture include all alternating hyperbolic knots with at most 16 crossings, 2-bridge links, and links that are closures of 3-strand braids. We improve Burton’s bound on the number of crossings for which the Vol–Det Conjecture holds for links with more than eight twists. We also strengthen Stoimenow’s inequalities between hyperbolic volumes and determinants for alternating and arborescent (Conway-algebraic) alternating links with more than eight twists.
Vesnin et al. (Sun,) studied this question.
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