Coloring links by the symmetric group of degree three

2021/12/05 by Ichihara, Kazuhiro, Matsudo, Eri
#FOS: Mathematics #Geometric Topology (math.GT)

paper · doi:10.48550/arxiv.2112.02515

Abstract

We consider the number of colors for the colorings of links by the symmetric group S₃ of degree 3. For knots, such a coloring corresponds to a Fox 3-coloring, and thus the number of colors must be 1 or 3. However, for links, there are colorings by S₃ with 4 or 5 colors. In this paper, we show that if a 2-bridge link admits a coloring by S₃ with 5 colors, then the link also admits such a coloring with only 4 colors.

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