Rank-Expanding Satellite Operators on the Topological Knot Concordance Group

Given a knot P⊂S1×B2 and a knot K⊂S3, we can form the satellite of K with pattern P, denoted P(K). This operation induces a self-map of the concordance group of knots in S3. It has been proved by Dai, Hedden, Mallick, and Stoffregen that in the smooth category, there exists P for which this function is rank-expanding, that is, for some K, the set {P(nK)}n∈Z generates an infinite-rank subgroup. Here we demonstrate that similar examples exist in the case of the topological locally flat concordance group. Such examples cannot exist in the algebraic concordance group.