Volume 19, issue 7 (2019)

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Upsilon-type concordance invariants

Antonio Alfieri

Algebraic & Geometric Topology 19 (2019) 3315–3334

To a region C of the plane satisfying a suitable convexity condition we associate a knot concordance invariant ϒC. For appropriate choices of the domain this construction gives back some known knot Floer concordance invariants like Rasmussen’s hi invariants, and the Ozsváth–Stipsicz–Szabó upsilon invariant. Furthermore, to three such regions C, C+ and C we associate invariants ϒC±,C generalizing the Kim–Livingston secondary invariant. We show how to compute these invariants for some interesting classes of knots (including alternating and torus knots), and we use them to obstruct concordances to Floer thin knots and algebraic knots.

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knot Floer homology, upsilon invariant, $L$–space knots
Mathematical Subject Classification 2010
Primary: 57M27
Received: 7 December 2017
Revised: 14 November 2018
Accepted: 2 December 2018
Published: 17 December 2019
Antonio Alfieri
Alfréd Rényi Institute of Mathematics