Alexander Matrices of Link Quandles Associated to Quandle Homomorphisms and Quandle Cocycle Invariants

Abstract

Ishii and Oshiro introduced the notion of an $f$-twisted Alexander matrix, which is a quandle version of a twisted Alexander matrix of finitely presented groups. In this paper, we study the relation between $f$-twisted Alexander matrices of link quandles and quandle cocycle invariants. We show that certain information of the quandle cocycle invariant can be recovered from the $f$-twisted Alexander matrix. As an application, we show that an invariant obtained from $f$-twisted Alexander matrices is a strictly stronger invariant for oriented knots than the twisted Alexander polynomial.