Finite $n$-quandles of torus and two-bridge links

TL;DR

This paper computes Cayley graphs and automorphism groups for all finite n-quandles associated with two-bridge and torus knots and links, providing detailed algebraic structures of these quandles.

Contribution

It offers a comprehensive analysis of finite n-quandles for specific classes of knots and links, including explicit computations of their Cayley graphs and automorphism groups.

Findings

Cayley graphs of finite n-quandles are explicitly characterized.

Automorphism groups of these quandles are determined.

Results apply to torus links with an axis as well.

Abstract

We compute Cayley graphs and automorphism groups for all finite $n$-quandles of two-bridge and torus knots and links, as well as torus links with an axis.