Volume 14, issue 2 (2010)

 Recent Issues
 The Journal About the Journal Editorial Board Editorial Interests Editorial Procedure Submission Guidelines Submission Page Subscriptions Author Index To Appear Contacts ISSN (electronic): 1364-0380 ISSN (print): 1465-3060
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