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A lower bound on the stable $4$–genus of knots

Damian Iltgen

Algebraic & Geometric Topology 22 (2022) 2239–2265
Abstract

We present a lower bound on the stable 4–genus of a knot based on Casson–Gordon τ–signatures. We compute the lower bound for an infinite family of knots, the twist knots, and show that a twist knot is torsion in the knot concordance group if and only if it has vanishing stable 4–genus.

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Keywords
low-dimensional topology, knot theory, stable $4$–genus, concordance group, twist knots
Mathematical Subject Classification
Primary: 57K10
References
Publication
Received: 17 June 2020
Revised: 16 April 2021
Accepted: 12 May 2021
Published: 25 October 2022
Authors
Damian Iltgen
Fakultät für Mathematik
Universität Regensburg
Regensburg
Germany