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 long 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.
The first author is partially supported by the ANR project COSPIN (ANR-13-JS01-0008-01). The second author is supported by the grant KAW 2013.0321 from the Knut and Alice Wallenberg Foundation. The fourth author is supported by the ESF Short Visit Grant, by the ERC Advanced Grant “LDTBud” and by the ERC Consolidator Grant 646649 “SymplecticEinstein”.
Baptiste Chantraine. Georgios Dimitroglou Rizell. Paolo Ghiggini. Roman Golovko. "Floer theory for Lagrangian cobordisms." J. Differential Geom. 114 (3) 393 - 465, March 2020. https://doi.org/10.4310/jdg/1583377213