A lower bound on the stable 4–genus of knots

Iltgen, Damian

doi:10.2140/agt.2022.22.2239

Download this article
	For screen
	For printing

Recent Issues

The Journal

About the Journal

Editorial Board

Editorial Interests

Subscriptions

Submission Guidelines

Submission Page

Policies for Authors

Ethics Statement

ISSN (electronic): 1472-2739

ISSN (print): 1472-2747

Author Index

To Appear

Other MSP Journals

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)