Comptes Rendus
Geometry and Topology
Doubly slice knots and obstruction to Lagrangian concordance
Comptes Rendus. Mathématique, Volume 361 (2023), pp. 1605-1609.

In this short note we observe that a result of Eliashberg and Polterovitch allows to use the doubly slice genus as an obstruction for a Legendrian knot to be a slice of a Lagrangian concordance from the trivial Legendrian knot with maximal Thurston–Bennequin invariant to itself. This allows to obstruct concordances from the Pretzel knot P(3,-3,-m) when m4 to the unknot. Those examples are of interest because the Legendrian contact homology algebra cannot be used to obstruct such a concordance.

Dans cette note, nous remarquons qu’un résultat d’Eliashberg et Polterovitch permet d’utiliser la notion de nœuds doublement bordant afin d’obstruer la possibilité pour un noeud legendrien d’apparaitre comme une tranche dans une concordance lagrangienne du noeud legendrien trivial d’invariant de Thurston–Bennequin maximal vers lui-même. Cela permet d’obstruer l’existence pour m4 de concordances du noeud pretzel P(3,-3,-m) vers le noeud trivial. Ces exemples s’avèrent particulièrement intéressants car l’algèbre d’homologie de contact legendrienne ne permet pas d’obstruer une telle concordance.

Received:
Revised:
Accepted:
Published online:
DOI: 10.5802/crmath.478
Classification: 57K33, 57K10

Baptiste Chantraine 1; Noémie Legout 2

1 Nantes Université, CNRS, Laboratoire de Mathématiques Jean Leray, LMJL, UMR 6629, F-44000 Nantes, France
2 Uppsala University, Department of Mathematics, Box 480, 751 06 Uppsala, Sweden
License: CC-BY 4.0
Copyrights: The authors retain unrestricted copyrights and publishing rights
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Baptiste Chantraine; Noémie Legout. Doubly slice knots and obstruction to Lagrangian concordance. Comptes Rendus. Mathématique, Volume 361 (2023), pp. 1605-1609. doi : 10.5802/crmath.478. https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.5802/crmath.478/

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