Geodesic
Upsilon-type concordance invariants
Alfieri, Antonio1
1 Alfréd Rényi Institute of Mathematics, Budapest, Hungary
Algebraic and Geometric Topology, Tome 19 (2019) no. 7, pp. 3315-3334

Voir la notice de l'article provenant de la source Mathematical Sciences Publishers

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.

DOI : 10.2140/agt.2019.19.3315
Classification : 57M27
Keywords: knot Floer homology, upsilon invariant, $L$–space knots

Alfieri, Antonio 1

1 Alfréd Rényi Institute of Mathematics, Budapest, Hungary 
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Alfieri, Antonio. Upsilon-type concordance invariants. Algebraic and Geometric Topology, Tome 19 (2019) no. 7, pp. 3315-3334. doi: 10.2140/agt.2019.19.3315

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