TG-Hyperbolicity of Virtual Links
Abstract
We extend the theory of hyperbolicity of links in the 3-sphere to tg-hyperbolicity of virtual links, using the fact that the theory of virtual links can be translated into the theory of links living in closed orientable thickened surfaces. When the boundary surfaces are taken to be totally geodesic, we obtain a tg-hyperbolic structure with a unique associated volume. We prove that all virtual alternating links are tg-hyperbolic. We further extend tg-hyperbolicity to several classes of non-alternating virtual links. We then consider bounds on volumes of virtual links and include a table for volumes of the 116 nontrivial virtual knots of four or fewer crossings, all of which, with the exception of the trefoil knot, turn out to be tg-hyperbolic.
Cite
@article{arxiv.1904.06385,
title = {TG-Hyperbolicity of Virtual Links},
author = {Colin Adams and Or Eisenberg and Jonah Greenberg and Kabir Kapoor and Zhen Liang and Kate O'Connor and Natalia Pacheco-Tallaj and Yi Wang},
journal= {arXiv preprint arXiv:1904.06385},
year = {2019}
}
Comments
18 pages, 11 figures