Volume and Determinant Densities of Hyperbolic Rational Links

Colin Adams; Aaron Calderon; Xinyi Jiang; Alexander Kastner; Gregory Kehne; Nathaniel Mayer; Mia Smith

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arXiv · 1510.06050

Volume and Determinant Densities of Hyperbolic Rational Links

Colin Adams·Aaron Calderon·Xinyi Jiang·Alexander Kastner·Gregory Kehne·Nathaniel Mayer·Mia Smith

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Abstract

The volume density of a hyperbolic link is defined as the ratio of hyperbolic volume to crossing number. We study its properties and a closely-related invariant called the determinant density. It is known that the sets of volume densities and determinant densities of links are dense in the interval [0,v_{oct}]. We construct sequences of alternating knots whose volume and determinant densities both converge to any x in [0,v_{oct}]. We also investigate the distributions of volume and determinant densities for hyperbolic rational links, and establish upper bounds and density results for these invariants.

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BibTeX RIS

Colin Adams, Aaron Calderon, Xinyi Jiang, Alexander Kastner, Gregory Kehne, Nathaniel Mayer, Mia Smith. 2015-10-20. Volume and Determinant Densities of Hyperbolic Rational Links. https://arxiv.org/abs/1510.06050

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