Doubly slice knots and obstruction to Lagrangian concordance
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 obstr...
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| Format: | Article |
| Language: | English |
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Académie des sciences
2023-11-01
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| Series: | Comptes Rendus. Mathématique |
| Online Access: | https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.5802/crmath.478/ |
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| author | Chantraine, Baptiste Legout, Noémie |
| author_facet | Chantraine, Baptiste Legout, Noémie |
| author_sort | Chantraine, Baptiste |
| collection | DOAJ |
| description | 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 $m\ge 4$ to the unknot. Those examples are of interest because the Legendrian contact homology algebra cannot be used to obstruct such a concordance. |
| format | Article |
| id | doaj-art-218d1911676348289f3c89ebb3a69360 |
| institution | Kabale University |
| issn | 1778-3569 |
| language | English |
| publishDate | 2023-11-01 |
| publisher | Académie des sciences |
| record_format | Article |
| series | Comptes Rendus. Mathématique |
| spelling | doaj-art-218d1911676348289f3c89ebb3a693602025-02-07T11:11:47ZengAcadémie des sciencesComptes Rendus. Mathématique1778-35692023-11-01361G101605160910.5802/crmath.47810.5802/crmath.478Doubly slice knots and obstruction to Lagrangian concordanceChantraine, Baptiste0Legout, Noémie1Nantes Université, CNRS, Laboratoire de Mathématiques Jean Leray, LMJL, UMR 6629, F-44000 Nantes, FranceUppsala University, Department of Mathematics, Box 480, 751 06 Uppsala, SwedenIn 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 $m\ge 4$ to the unknot. Those examples are of interest because the Legendrian contact homology algebra cannot be used to obstruct such a concordance.https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.5802/crmath.478/ |
| spellingShingle | Chantraine, Baptiste Legout, Noémie Doubly slice knots and obstruction to Lagrangian concordance Comptes Rendus. Mathématique |
| title | Doubly slice knots and obstruction to Lagrangian concordance |
| title_full | Doubly slice knots and obstruction to Lagrangian concordance |
| title_fullStr | Doubly slice knots and obstruction to Lagrangian concordance |
| title_full_unstemmed | Doubly slice knots and obstruction to Lagrangian concordance |
| title_short | Doubly slice knots and obstruction to Lagrangian concordance |
| title_sort | doubly slice knots and obstruction to lagrangian concordance |
| url | https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.5802/crmath.478/ |
| work_keys_str_mv | AT chantrainebaptiste doublysliceknotsandobstructiontolagrangianconcordance AT legoutnoemie doublysliceknotsandobstructiontolagrangianconcordance |