Multivariate Alexander quandles, IV. The medial quandle of a link

Abstract

Joyce observed that the Alexander invariant and the medial quandle of a classical knot are equivalent to each other, as invariants. In the present paper, we discuss the rather complicated extension of Joyce's observation to several different medial quandles and reduced (one-variable) Alexander modules associated with classical links. The theme is that for links, medial quandles provide stronger invariants than reduced Alexander modules.

arXiv commentv1: 33 pages, 7 figures. v2: minor edits. v3: 43 pages, 9 figures. major revision, including corrected interpretation of results of Joyce. v4: minor edits