A lower bound on the stable 4–genus of knots

Iltgen, Damian

doi:10.2140/agt.2022.22.2239

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

Damian Iltgen

Algebraic & Geometric Topology 22 (2022) 2239–2265

DOI: 10.2140/agt.2022.22.2239

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.

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

Volume 22, issue 5 (2022)