Iterated satellite operators on the knot concordance group

We show that for a winding number zero satellite operator P on the knot concordance group, if the axis of P has nontrivial self-pairing under the Blanchfield form of the pattern, then the image of the iteration Pn generates an infinite rank subgroup for each n. Furthermore, the graded quotients of the filtration of the knot concordance group associated with P have infinite rank at all levels. This gives an affirmative answer to a question of Hedden and Pinz & oacute;n-Caicedo in many cases. We also show that under the same hypotheses, Pn is not a homomorphism on the knot concordance group for each n. We use amenable L2-signatures to prove these results. (c) 2025 Elsevier Inc. All rights are reserved, including those for text and data mining, AI training, and similar technologies.