Floer theory for Lagrangian cobordisms
Symplectic Geometry
2025-02-07 v4
Abstract
In this article we define intersection Floer homology for exact Lagrangian cobordisms between Legendrian submanifolds in the contactisation of a Liouville manifold, provided that the Chekanov-Eliashberg algebras of the negative ends of the cobordisms admit augmentations. From this theory we derive several exact sequences relating the Morse homology of an exact Lagrangian cobordism with the bilinearised contact homologies of its ends. These are then used to investigate the topological properties of exact Lagrangian cobordisms.
Cite
@article{arxiv.1511.09471,
title = {Floer theory for Lagrangian cobordisms},
author = {Baptiste Chantraine and Georgios Dimitroglou Rizell and Paolo Ghiggini and Roman Golovko},
journal= {arXiv preprint arXiv:1511.09471},
year = {2025}
}
Comments
61 pages, 17 figures. Final version, accepted for publication in Journal of Differential Geometry, some missing citations have been added