Rank-expanding satellite operators on the topological knot concordance group

Charles Livingston

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arXiv · 2211.04272

Rank-expanding satellite operators on the topological knot concordance group

Charles Livingston

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Abstract

Given a fixed knot P in a solid torus and any knot K in S^3, one can form the satellite of K with pattern P. This operation induces a self-map of the concordance group of knots in S^3. It has been proved by Dai, Hedden, Mallick, and Stoffregen that in the smooth category there exist P for which this function is rank-expanding; that is, for some K, the set {P(nK)} 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.

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Charles Livingston. 2022-11-08. Rank-expanding satellite operators on the topological knot concordance group. https://arxiv.org/abs/2211.04272

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