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2019 Upsilon-type concordance invariants
Antonio Alfieri
Algebr. Geom. Topol. 19(7): 3315-3334 (2019). 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 ± , 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.

Citation

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Antonio Alfieri. "Upsilon-type concordance invariants." Algebr. Geom. Topol. 19 (7) 3315 - 3334, 2019. https://doi.org/10.2140/agt.2019.19.3315

Information

Received: 7 December 2017; Revised: 14 November 2018; Accepted: 2 December 2018; Published: 2019
First available in Project Euclid: 3 January 2020

zbMATH: 07162208
MathSciNet: MR4045354
Digital Object Identifier: 10.2140/agt.2019.19.3315

Subjects:
Primary: 57M27

Rights: Copyright © 2019 Mathematical Sciences Publishers

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Vol.19 • No. 7 • 2019
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