Multivariate Alexander quandles, IV. The medial quandle of a link
Lorenzo Traldi
TL;DR
This paper explores the relationship between medial quandles and Alexander modules in classical links, demonstrating that medial quandles serve as stronger invariants than reduced Alexander modules.
Contribution
It extends Joyce's observation from knots to links, showing medial quandles offer more powerful invariants than reduced Alexander modules.
Findings
Medial quandles provide stronger invariants for links.
Extension of Joyce's knot invariants to links.
Medial quandles and Alexander modules are related but differ in strength.
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.
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Taxonomy
TopicsGeometric and Algebraic Topology