Ribbon concordance of knots is a partial ordering

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 S O ( N ) SO(N) and the subquotient relation between them induced by a ribbon concordance.