2025 Rank-Expanding Satellite Operators on the Topological Knot Concordance Group
Charles Livingston
Michigan Math. J. Advance Publication 1-9 (2025). DOI: 10.1307/mmj/20236417

Abstract

Given a knot PS1×B2 and a knot KS3, 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)}nZ 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. "Rank-Expanding Satellite Operators on the Topological Knot Concordance Group." Michigan Math. J. Advance Publication 1 - 9, 2025. https://doi.org/10.1307/mmj/20236417

Information

Received: 31 July 2023; Revised: 1 November 2023; Published: 2025
First available in Project Euclid: 24 January 2025

Digital Object Identifier: 10.1307/mmj/20236417

Keywords: 57K10

Rights: Copyright © 2024 The University of Michigan

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