# Ribbon n-knots with isomorphic quandles

## TL;DR

This paper proves that for ribbon knottings of n-spheres with 1-handles in higher-dimensional spheres, isomorphic quandles imply stable equivalence after finitely many trivial connected sums.

## Contribution

It establishes a link between quandle isomorphisms and stable equivalence of ribbon knottings in higher dimensions, extending previous understanding.

## Key findings

- Isomorphic knot quandles imply stable equivalence after trivial sums.
- The result applies to ribbon knottings of n-spheres with 1-handles.
- Provides a new criterion for knot equivalence in higher dimensions.

## Abstract

Let $K, K'$ be ribbon knottings of $n$-spheres with $1$-handles in $S^{n+2}$, $n\geq 2$. We show that if the knot quandles of these knots are isomorphic, then the ribbon knottings are stably equivalent, in the sense of Nakanishi and Nakagawa, after taking a finite number of connected sums with trivially embedded copies of $S^{n-1}\times S^{1}$.