Multivariate Alexander quandles, II. The involutory medial quandle of a link (corrected)

Abstract

Joyce showed that for a classical knot [Formula: see text], the involutory medial quandle [Formula: see text] is isomorphic to the core quandle of the homology group [Formula: see text], where [Formula: see text] is the cyclic double cover of [Formula: see text], branched over [Formula: see text]. It follows that [Formula: see text]. In this paper, the extension of Joyce’s result to classical links is discussed. Among other things, we show that for a classical link [Formula: see text] of [Formula: see text] components, the order of the involutory medial quandle is bounded as follows: [Formula: see text] In particular, [Formula: see text] is infinite if and only if [Formula: see text]. We also show that in general, [Formula: see text] is a strictly stronger invariant than [Formula: see text]. That is, if [Formula: see text] and [Formula: see text] are links with [Formula: see text], then [Formula: see text]; but it is possible to have [Formula: see text] and [Formula: see text]. In fact, it is possible to have [Formula: see text] and [Formula: see text].