$2$-knots with the same knot group but different knot quandles

TL;DR

This paper presents the first example of 2-knots sharing the same knot group but having different knot quandles, and classifies twist spins with finite knot quandles.

Contribution

It introduces the first known example of 2-knots with identical knot groups but distinct knot quandles, and provides a classification of twist spins with finite quandles.

Findings

Identified 2-knots with same group but different quandles

Classified all twist spins with finite knot quandles

Analyzed knot quandles of twist spins

Abstract

We give a first example of 2-knots with the same knot group but different knot quandles by analyzing the knot quandles of twist spins. As a byproduct of the analysis, we also give a classification of all twist spins with finite knot quandles.