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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
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.

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