Homological Polynomial Coefficients and the Twist Number of Alternating Surface Links

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.

References in corpus (1)

• Non-triviality of the Jones polynomial and the crossing numbers of amphicheiral knots

Cited by in corpus (1)

• Adequate links in thickened surfaces and the generalized Tait conjectures