Georgia Institute of Technology College of Sciences

A knot is slice if it bounds a smoothly embedded disk in the four-ball and a knot is ribbon if it bounds such a disk with no local maxima. The slice-ribbon conjecture posits that every slice knot is ribbon. We prove that a linear combination of iterated cables of tight fibered knots is ribbon if and only if it is of the form K # -K, generalizing work of Miyazaki and Baker. Consequently, either iterated cables of tight fibered knots are linearly independent in the smooth concordance group, or the slice–ribbon conjecture fails.