COLORING LINK DIAGRAMS BY ALEXANDER QUANDLES

Abstract

In this paper, we study the colorability of link diagrams by the Alexander quandles. We show that if the reduced Alexander polynomial ΔL(t) is vanishing, then L admits a non-trivial coloring by any non-trivial Alexander quandle Q, and that if ΔL(t) = 1, then L admits only the trivial coloring by any Alexander quandle Q, also show that if ΔL(t) ≠ 0, 1, then L admits a non-trivial coloring by the Alexander quandle Λ/(ΔL(t)).