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arXiv · 1501.04258

Floer homology and Lagrangian concordance

Baptiste Chantraine·Georgios Dimitroglou Rizell·Paolo Ghiggini·Roman Golovko
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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.

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Baptiste Chantraine, Georgios Dimitroglou Rizell, Paolo Ghiggini, Roman Golovko. 2015-01-18. Floer homology and Lagrangian concordance. https://arxiv.org/abs/1501.04258

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