Multivariate Alexander quandles, III. Sublinks

2019/05/20 by Traldi, Lorenzo
#FOS: Mathematics #Geometric Topology (math.GT)

paper · doi:10.48550/arxiv.1905.07965

Abstract

If L is a classical link then the multivariate Alexander quandle, Q_A(L), is a substructure of the multivariate Alexander module, M_A(L). In the first paper of this series we showed that if two links L and L' have Q_A(L) ≅ Q_A(L'), then after an appropriate re-indexing of the components of L and L', there will be a module isomorphism M_A(L) ≅ M_A(L') of a particular type, which we call a"Crowell equivalence." In the present paper we show that Q_A(L) (up to quandle isomorphism) is a strictly stronger link invariant than M_A(L) (up to re-indexing and Crowell equivalence). This result follows from the fact that Q_A(L) determines the Q_A quandles of all the sublinks of L, up to quandle isomorphisms.

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