On the knot quandle of a fibered knot, finiteness and equivalence of knot quandles

TL;DR

This paper explores how the fibered structure of knots influences their knot quandles, focusing on finiteness and equivalence, especially for fibered 2-knots, revealing structural insights and classification criteria.

Contribution

It demonstrates the reflection of fibered knot structures in their quandles and discusses finiteness and equivalence of knot quandles for fibered 2-knots, providing new understanding.

Findings

Fibered knot structure is reflected in its knot quandle.

Finiteness of knot quandles is characterized for fibered 2-knots.

Conditions for quandle equivalence are established for fibered 2-knots.

Abstract

We show that the structure of a fibered knot, as a fiber bundle, is reflected in its knot quandle. As an application, we discuss finiteness and equivalence of knot quandles of concrete fibered 2-knots.