Ribbon n-knots with isomorphic quandles

Abstract

Let $K,K^{\prime }$ be ribbon knottings of $n$-spheres with $1$-handles in $S^{n+2}$, $n\ge 2$. 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 $S^{n-1}\times S^1$.