Homological Polynomial Coefficients and the Twist Number of Alternating Surface Links

David A. Will

doi:10.2140/agt.2022.22.3939

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arXiv · 2011.12274

Homological Polynomial Coefficients and the Twist Number of Alternating Surface Links

David A. Will

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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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David A. Will. 2020-11-24. Homological Polynomial Coefficients and the Twist Number of Alternating Surface Links. https://doi.org/10.2140/agt.2022.22.3939

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