#### 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 $\Upsilon$, although their secondary Upsilon invariants ${\Upsilon }^{2}$ 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
Primary: 57R58