Ribbon n-knots with isomorphic quandles

2017/01/31 by Blake Winter, Winter, Blake Karl
Mathematics · #Geometric and Algebraic Topology #Homotopy and Cohomology in Algebraic Topology #Mathematical Dynamics and Fractals

paper · pdf · doi:10.48550/arxiv.1702.00086

Abstract

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 S^n-1× S¹.

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