English

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