Densities of Hyperbolic Cusp Invariants
Geometric Topology
2017-01-16 v1
Abstract
We find that cusp densities of hyperbolic knots in the 3-sphere are dense in [0,0.6826...] and those of links are dense in [0,0.853...]. We define a new invariant associated with cusp volume, the cusp crossing density, as the ratio between the cusp volume and the crossing number of a link, and show that cusp crossing density for links is bounded above by 3.1263.... Moreover, there is a sequence of links with cusp crossing density approaching 3. The least upper bound for cusp crossing density remains an open question. For two-component hyperbolic links, cusp crossing density is shown to be dense in the interval [0,1.6923...] and for all hyperbolic links, cusp crossing density is shown to be dense in [0, 2.120...].
Cite
@article{arxiv.1701.03479,
title = {Densities of Hyperbolic Cusp Invariants},
author = {Colin Adams and Rose Kaplan-Kelly and Michael Moore and Brandon Shapiro and Shruthi Sridhar and Joshua Wakefield},
journal= {arXiv preprint arXiv:1701.03479},
year = {2017}
}
Comments
17 pages, 12 figures