Upsilon-type concordance invariants

Alfieri, Antonio

doi:10.2140/agt.2019.19.3315

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Upsilon-type concordance invariants

Antonio Alfieri

Algebraic & Geometric Topology 19 (2019) 3315–3334

DOI: 10.2140/agt.2019.19.3315

Abstract

To a region $C$ of the plane satisfying a suitable convexity condition we associate a knot concordance invariant $ϒ^{C}$ . For appropriate choices of the domain this construction gives back some known knot Floer concordance invariants like Rasmussen’s $h_{i}$ invariants, and the Ozsváth–Stipsicz–Szabó upsilon invariant. Furthermore, to three such regions $C$ , $C^{+}$ and $C^{-}$ we associate invariants $ϒ_{C^{\pm}, C}$ 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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Keywords

knot Floer homology, upsilon invariant, $L$–space knots

Mathematical Subject Classification 2010

Primary: 57M27

References

Publication

Received: 7 December 2017

Revised: 14 November 2018

Accepted: 2 December 2018

Published: 17 December 2019

Authors

Antonio Alfieri
Alfréd Rényi Institute of Mathematics Budapest Hungary

Volume 19, issue 7 (2019)