On the Upsilon invariant of cable knots

Chen, Wenzhao

doi:10.2140/agt.2021.21.1075

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

This article is available for purchase or by subscription. See below.

On the Upsilon invariant of cable knots

Wenzhao Chen

Algebraic & Geometric Topology 21 (2021) 1075–1092

DOI: 10.2140/agt.2021.21.1075

Abstract

We study the behavior of $ϒ_{K} (t)$ under the cabling operation, where $ϒ_{K} (t)$ is the knot concordance invariant defined by Ozsváth, Stipsicz, and Szabó, associated to a knot $K \subset S^{3}$ . The main result is an inequality relating $ϒ_{K} (t)$ and $ϒ_{K_{p, q}} (t)$ , where $K_{p, q}$ 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 $ϒ_{{(T_{2, - 3})}_{2, 2 n + 1}} (t)$ for $n \geq 8$ , and we show that the set of iterated $(p, 1)$ –cables of ${Wh}^{+} (T_{2, 3})$ for any $p \geq 2$ span an infinite-rank summand of topologically slice knots.

PDF Access Denied

We have not been able to recognize your IP address 3.133.121.160 as that of a subscriber to this journal.
Online access to the content of recent issues is by subscription, or purchase of single articles.

Please contact your institution's librarian suggesting a subscription, for example by using our journal-recommendation form. Or, visit our subscription page for instructions on purchasing a subscription.

You may also contact us at contact@msp.org
or by using our contact form.

Or, you may purchase this single article for USD 40.00:

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

Volume 21, issue 3 (2021)