Volume 21, issue 3 (2021)

Download this article
Download this article For screen
For printing
Recent Issues

Volume 21
Issue 4, 1595–2140
Issue 3, 1075–1593
Issue 2, 543–1074
Issue 1, 1–541

Volume 20, 7 issues

Volume 19, 7 issues

Volume 18, 7 issues

Volume 17, 6 issues

Volume 16, 6 issues

Volume 15, 6 issues

Volume 14, 6 issues

Volume 13, 6 issues

Volume 12, 4 issues

Volume 11, 5 issues

Volume 10, 4 issues

Volume 9, 4 issues

Volume 8, 4 issues

Volume 7, 4 issues

Volume 6, 5 issues

Volume 5, 4 issues

Volume 4, 2 issues

Volume 3, 2 issues

Volume 2, 2 issues

Volume 1, 2 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
On the Upsilon invariant of cable knots

Wenzhao Chen

Algebraic & Geometric Topology 21 (2021) 1075–1092
Abstract

We study the behavior of ϒK(t) under the cabling operation, where ϒK(t) is the knot concordance invariant defined by Ozsváth, Stipsicz, and Szabó, associated to a knot K S3. The main result is an inequality relating ϒK(t) and ϒKp,q(t), where Kp,q denotes the (p,q)–cable of K. This result generalizes the inequalities of Hedden and Van Cott on the Ozsváth–Szabó τ–invariant. As applications, we give a computation of ϒ(T2,3)2,2n+1(t) for n 8, and we show that the set of iterated (p,1)–cables of Wh+(T2,3) for any p 2 span an infinite-rank summand of topologically slice knots.

Keywords
Upsilon invariant, knot concordance, cable, knot Floer homology
Mathematical Subject Classification 2010
Primary: 57M25, 57R58
References
Publication
Received: 9 August 2017
Accepted: 19 July 2020
Published: 11 August 2021
Authors
Wenzhao Chen
Max Planck Institute for Mathematics
Bonn
Germany