2019/01/08 by H. S. Allen, Allen, Heidi, Ryan Blair +3
Mathematics · #Geometric and Algebraic Topology
paper · pdf · doi:10.48550/arxiv.1901.02558
It was previously shown by the second author that every knot in S3 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.