Multivariate Alexander quandles, VI. Metabelian groups and 2-component links

Abstract

We prove two properties of the modules and quandles discussed in this series. First, the fundamental multivariate Alexander quandle $Q_A(L)$ is isomorphic to the natural image of the fundamental quandle in the metabelian quotient $G(L)/G(L{)}^{\prime \prime }$ of the link group. Second, the medial quandle of a classical 2-component link $L$ is determined by the reduced Alexander invariant of $L$.

v1: 11 pages, one figure. v2: minor edits