A volumish theorem for alternating virtual links

Abhijit Champanerkar; Ilya Kofman

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arXiv · 2010.08499

A volumish theorem for alternating virtual links

Abhijit Champanerkar·Ilya Kofman

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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.

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Abhijit Champanerkar, Ilya Kofman. 2020-10-16. A volumish theorem for alternating virtual links. https://arxiv.org/abs/2010.08499

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