Coloring link diagrams by Alexander quandles

Details Coloring link diagrams by Alexander quandles Coloring link diagrams by Alexander quandles

2011-05-18

arxiv.org/abs/1105.3695v1

Mathematics

Geometric Topology

13 pages, 1 figure

Scientific paper

In this paper, we study the colorability of link diagrams by the Alexander quandles. We show that if the reduced Alexander polynomial $\Delta_{L}(t)$ is vanishing, then $L$ admits a non-trivial coloring by any non-trivial Alexander quandle $Q$, and that if $\Delta_{L}(t)=1$, then $L$ admits only the trivial coloring by any Alexander quandle $Q$, also show that if $\Delta_{L}(t)\not=0, 1$, then $L$ admits a non-trivial coloring by the Alexander quandle $\Lambda/(\Delta_{L}(t))$.

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