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arXiv · 1901.02558

Twist Number and the Alternating Volume of Knots

Heidi Allen·Ryan Blair·Leslie Rodriguez
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Abstract

It was previously shown by the second author that every knot in $S^3$ is ambient isotopic to one component of a two-component, alternating, hyperbolic link. In this paper, we define the alternating volume of a knot $K$ to be the minimum volume of any link $L$ in a natural class of alternating, hyperbolic links such that $K$ is ambient isotopic to a component of $L$. Our main result shows that the alternating volume of a knot is coarsely equivalent to the twist number of a knot.

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Heidi Allen, Ryan Blair, Leslie Rodriguez. 2019-01-08. Twist Number and the Alternating Volume of Knots. https://arxiv.org/abs/1901.02558

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