2011/05/18 by Yongju Bae, Bae, Yongju
Mathematics · #57M25 #Advanced Combinatorial Mathematics #Algebraic structures and combinatorial models #FOS: Mathematics #Geometric Topology (math.GT) #Geometric and Algebraic Topology #math.GT #msc:57M25
paper · pdf · doi:10.48550/arxiv.1105.3695
13 pages, 1 figure
arxiv created 2011/05/18 · openalex publication_date 2011/05/18 · arxiv updated 2011/05/19 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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)\not=0, 1, then L admits a non-trivial coloring by the Alexander quandle Λ/(ΔL(t)).