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Abstract

In this note we show that ribbon concordance forms a partial ordering on the set of knots, answering a question of Gordon [Math. Ann. 257 (1981), pp. 157-170, Conjecture 1.1]. The proof makes use of representation varieties of the knot groups to 𝑆𝑂(𝑁) and the subquotient relation between them induced by a ribbon concordance.