Two-tone colorings and surjective dihedral representations for links
Geometric Topology
2024-04-30 v3
Abstract
It is well-known that a knot is Fox -colorable for a prime if and only if the knot group admits a surjective homomorphism to the dihedral group of degree . 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.
Keywords
Cite
@article{arxiv.2302.13706,
title = {Two-tone colorings and surjective dihedral representations for links},
author = {Kazuhiro Ichihara and Katsumi Ishikawa and Eri Matsudo and Masaaki Suzuki},
journal= {arXiv preprint arXiv:2302.13706},
year = {2024}
}
Comments
13 pages, 6 figures. Several improvements based on the referees' comments