Ribbon n-knots with isomorphic quandles

Original · EN

Let K, K' be ribbon knottings of n-spheres with 1-handles in Sⁿ⁺², n≥ 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 Sⁿ⁻¹× S¹.