Homological polynomial coefficients and the twist number of alternating surface links

Will, David A

doi:10.2140/agt.2022.22.3939

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Homological polynomial coefficients and the twist number of alternating surface links

David A Will

Algebraic & Geometric Topology 22 (2022) 3939–3963

DOI: 10.2140/agt.2022.22.3939

Abstract

For $D$ a reduced alternating surface link diagram, we bound the twist number of $D$ in terms of the coefficients of a polynomial invariant. To this end, we introduce a generalization of the homological Kauffman bracket defined by Krushkal. Combined with work of Futer, Kalfagianni and Purcell, this yields a bound for the hyperbolic volume of a class of alternating surface links in terms of these coefficients.

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Keywords

links in thickened surfaces, Kauffman bracket, twist number, hyperbolic volume

Mathematical Subject Classification

Primary: 57K10

Secondary: 57K32

References

Publication

Received: 14 December 2020

Revised: 9 August 2021

Accepted: 7 September 2021

Published: 14 March 2023

Authors

David A Will
Department of Mathematics University of Virginia Charlottesville, VA United States

Volume 22, issue 8 (2022)