English

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.

Keywords

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

R2 v1 2026-06-23T19:24:29.306Z