Coloring Torus Knots by Conjugation Quandles
Filippo Spaggiari

TL;DR
This paper investigates how torus knots can be colored using conjugation quandles over various groups, providing general results and specific numerical criteria for certain groups like matrix groups, dihedral, and symmetric groups.
Contribution
It offers new theoretical insights into the colorability of torus knots with conjugation quandles and provides explicit numerical characterizations for specific groups.
Findings
General results on torus knot colorability with conjugation quandles
Numerical criteria for colorability over $GL(2,q)$, $SL(2,q)$, dihedral, and symmetric groups
Enhanced understanding of knot invariants via group-based colorings
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 and , the dihedral group, and the symmetric group.
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Taxonomy
TopicsGeometric and Algebraic Topology · Homotopy and Cohomology in Algebraic Topology · semigroups and automata theory
