GÖKOVA GEOMETRY / TOPOLOGY PROCEEDINGS |
Published in |
Proceedings of Gökova Geometry-Topology Conference 2014 |
Title |
Floer homology and Lagrangian concordance |
Authors |
Baptiste Chantraine, Georgios Dimitroglou Rizell, Paolo Ghiggini, and Roman Golovko |
Abstract |
We derive constraints on Lagrangian concordances from Legendrian submanifolds of the standard contact sphere admitting exact Lagrangian fillings. More precisely, we show that such a concordance induces an isomorphism on the level of bilinearised Legendrian contact cohomology. This is used to prove the existence of non-invertible exact Lagrangian concordances in all dimensions. In addition, using a result of Eliashberg-Polterovich, we completely classify exact Lagrangian concordances from the Legendrian unknot to itself in the tight contact-three sphere: every such concordance is the trace of a Legendrian isotopy. We also discuss a high dimensional topological result related to this classification. |
Keywords |
Lagrangian concordance, Floer homology, Legendrian unknot, non-symmetry
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Pages | 76-113 |
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