A volumish theorem for alternating virtual links
Geometric Topology
2025-05-12 v2
Abstract
Dasbach and Lin proved a "volumish theorem" for alternating links. We prove the analogue for alternating link diagrams on surfaces, which provides bounds on the hyperbolic volume of a link in a thickened surface in terms of coefficients of its reduced Jones-Krushkal polynomial. Along the way, we show that certain coefficients of the 4-variable Krushkal polynomial express the cycle rank of the reduced Tait graph on the surface.
Cite
@article{arxiv.2010.08499,
title = {A volumish theorem for alternating virtual links},
author = {Abhijit Champanerkar and Ilya Kofman},
journal= {arXiv preprint arXiv:2010.08499},
year = {2025}
}
Comments
17 pages. v2: minor corrections