#### Volume 14, issue 2 (2010)

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Quilted Floer cohomology

### Katrin Wehrheim and Chris T Woodward

Geometry & Topology 14 (2010) 833–902
##### Abstract

We generalize Lagrangian Floer cohomology to sequences of Lagrangian correspondences. For sequences related by the geometric composition of Lagrangian correspondences we establish an isomorphism of the Floer cohomologies. This provides the foundation for the construction of a symplectic $2$–category as well as for the definition of topological invariants via decomposition and representation in the symplectic category. Here we give some first direct symplectic applications: Calculations of Floer cohomology, displaceability of Lagrangian correspondences and transfer of displaceability under geometric composition.

##### Keywords
Floer theory, Lagrangian correspondence, Hamiltonian nondisplaceability
Primary: 53D40
Secondary: 57R56