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March 2020 Floer theory for Lagrangian cobordisms
Baptiste Chantraine, Georgios Dimitroglou Rizell, Paolo Ghiggini, Roman Golovko
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J. Differential Geom. 114(3): 393-465 (March 2020). DOI: 10.4310/jdg/1583377213


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.

Funding Statement

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”.


Download Citation

Baptiste Chantraine. Georgios Dimitroglou Rizell. Paolo Ghiggini. Roman Golovko. "Floer theory for Lagrangian cobordisms." J. Differential Geom. 114 (3) 393 - 465, March 2020.


Received: 24 June 2016; Published: March 2020
First available in Project Euclid: 5 March 2020

zbMATH: 07179184
MathSciNet: MR4072203
Digital Object Identifier: 10.4310/jdg/1583377213

Rights: Copyright © 2020 Lehigh University


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Vol.114 • No. 3 • March 2020
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