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

2024/08/21 by Traldi, Lorenzo
#FOS: Mathematics #Geometric Topology (math.GT)

paper · doi:10.48550/arxiv.2408.11784

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)'' of the link group. Second, the medial quandle of a classical 2-component link L is determined by the reduced Alexander invariant of L.

Related

• Multivariate Alexander quandles, III. Sublinks
• Multivariate Alexander quandles, I. The module sequence of a link
• Multivariate Alexander quandles, IV. The medial quandle of a link
• Multivariate Alexander quandles, V. Constructing the medial quandle of a link
• Multivariate Alexander quandles, II. The involutory medial quandle of a link (corrected)