Alexander Polynomials of closed alternating braids

Mark E. AlSukaiti; Nafaa Chbili

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arXiv · 2310.14539

Alexander Polynomials of closed alternating braids

Mark E. AlSukaiti·Nafaa Chbili

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Abstract

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.

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Mark E. AlSukaiti, Nafaa Chbili. 2023-10-23. Alexander Polynomials of closed alternating braids. https://arxiv.org/abs/2310.14539

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