Volume 21, issue 4 (2021)

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On the secondary Upsilon invariant

Xiaoyu Xu

Algebraic & Geometric Topology 21 (2021) 1661–1676
Abstract

We construct an infinite family of knots with vanishing Upsilon invariant ϒ, although their secondary Upsilon invariants ϒ2 show that they are linearly independent in the smooth knot concordance group. We also prove a conjecture of Allen.

Keywords
knot Floer homology, Upsilon invariant
Mathematical Subject Classification 2010
Primary: 57R58
References
Publication
Received: 13 April 2018
Revised: 29 May 2020
Accepted: 16 August 2020
Published: 18 August 2021
Authors
Xiaoyu Xu
Department of Mathematics
Princeton University
Princeton, NJ
United States