Alexander matrices of link quandles associated to quandle homomorphisms and quandle cocycle invariants

Yuta Taniguchi

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arXiv · 2107.06561

Alexander matrices of link quandles associated to quandle homomorphisms and quandle cocycle invariants

Yuta Taniguchi

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Abstract

A. Ishii and K. Oshiro introduced the notion of an $f$-twisted Alexander matrix. This notion is a quandle version of the twisted Alexander matrix which was introduced by M. Wada. They showed that the twisted Alexander matrix of a pair of a link group and a group representation can be recovered from the $f$-twisted Alexander matrix of a pair of a link quandle and a quandle homomorphism. In this paper, we study a relationship between the $f$-twisted Alexander matrix and the quandle cocycle invariant. As an application, we show that an $f$-twisted Alexander invariant of knot quandles is a really stronger oriented knot invariant than a twisted Alexander invariant of knot groups.

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Yuta Taniguchi. 2021-07-14. Alexander matrices of link quandles associated to quandle homomorphisms and quandle cocycle invariants. https://arxiv.org/abs/2107.06561

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