Volume 21, issue 3 (2021)

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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