Alexander Polynomials of closed alternating braids

We prove that the Alexander polynomials of certain families of alternating 4-braid knots satisfy Fox's Trapezoidal Conjecture. Moreover, we give explicit formulas for the signature and for the first 4 coefficients of the Alexander polynomial for a large family of alternating \(n\)-braid links a...

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Bibliographic Details
Published inarXiv.org
Main Authors AlSukaiti, Mark E, Chbili, Nafaa
Format Paper
LanguageEnglish
Published Ithaca Cornell University Library, arXiv.org 23.10.2023
Subjects
Braiding
Polynomials
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Summary:We prove that the Alexander polynomials of certain families of alternating 4-braid knots satisfy Fox's Trapezoidal Conjecture. Moreover, we give explicit formulas for the signature and for the first 4 coefficients of the Alexander polynomial for a large family of alternating \(n\)-braid links and we verify that these 4 coefficients form a log-concave sequence.
ISSN:2331-8422