Floer homology and Lagrangian concordance
Symplectic Geometry
2015-01-20 v1
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
Cite
@article{arxiv.1501.04258,
title = {Floer homology and Lagrangian concordance},
author = {Baptiste Chantraine and Georgios Dimitroglou Rizell and Paolo Ghiggini and Roman Golovko},
journal= {arXiv preprint arXiv:1501.04258},
year = {2015}
}
Comments
39 pages, 3 figures