Coloring Torus Knots by Conjugation Quandles

Filippo Spaggiari

Coloring Torus Knots by Conjugation Quandles

Group Theory 2023-08-22 v1

Authors: Filippo Spaggiari

Abstract

In the first part of this paper, we present general results concerning the colorability of torus knots using conjugation quandles over any abstract group. Subsequently, we offer a numerical characterization for the colorability of torus knots using conjugation quandles over some particular groups, such as the matrix groups $GL(2,q)$ and $SL(2,q)$ , the dihedral group, and the symmetric group.

Keywords

torus knots conjugation quandles knot coloring abstract group matrix groups dihedral group symmetric group

Cite

@article{arxiv.2308.10229,
  title  = {Coloring Torus Knots by Conjugation Quandles},
  author = {Filippo Spaggiari},
  journal= {arXiv preprint arXiv:2308.10229},
  year   = {2023}
}

Comments

13 pages, 4 figures

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