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arXiv · 1112.2335

Weights of Markov traces for Alexander polynomials of mixed links

Hitoshi Yamanaka
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Abstract

Using the Fourier expansion of Markov traces for Ariki-Koike algebras over $\mathbb{Q}(q,u_{1},...,u_{e})$, we give a direct definition of the Alexander polynomials for mixed links. We observe that under the corresponding specialization of a Markov parameter, the Fourier coefficients of Markov traces take quite simple form. As a consequence, we show that the Alexander polynomial of a mixed link is essentially equal to the Alexander polynomial of the link obtained by resolving the twisted parts.

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Hitoshi Yamanaka. 2011-12-11. Weights of Markov traces for Alexander polynomials of mixed links. https://arxiv.org/abs/1112.2335

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