2023/02/27 by Ichihara, Kazuhiro, Ishikawa, Katsumi, Matsudo, Eri +1 · 1 citation
#57K10 #FOS: Mathematics #Geometric Topology (math.GT)
paper · doi:10.48550/arxiv.2302.13706
It is well-known that a knot is Fox n-colorable for a prime n if and only if the knot group admits a surjective homomorphism to the dihedral group of degree n. However, this is not the case for links with two or more components. In this paper, we introduce a two-tone coloring on a link diagram, and give a condition for links so that the link groups admit surjective representations to the dihedral groups. In particular, it is shown that the link group of any link with at least 3 components admits a surjective homomorphism to the dihedral group of arbitrary degree.