Floer theory for Lagrangian cobordisms

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.

61 pages, 17 figures. Final version, accepted for publication in Journal of Differential Geometry, some missing citations have been added

References in corpus (4)

• Functors and Computations in Floer homology with Applications Part II
• Contact homology and virtual fundamental cycles
• Noncommutative augmentation categories
• Floer's chain complexes for Lagrangian submanifolds in symplectic manifolds with concave ends

Cited by in corpus (8)

• Geometric generation of the wrapped Fukaya category of Weinstein manifolds and sectors
• Chekanov-Eliashberg dg-algebras for singular Legendrians
• The persistence of a relative Rabinowitz-Floer complex
• Spherical twists and Lagrangian spherical manifolds
• Legendrian Satellites and Decomposable Concordances
• Homological invariants of codimension 2 contact submanifolds
• A-infinity category of Lagrangian cobordisms in the symplectization of PxR
• Lagrangian cobordism functor in microlocal sheaf theory I