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
Publication
Received: 14 May 2009
Revised: 4 January 2009
Accepted: 25 November 2009
Published: 5 March 2010
Proposed: Leonid Polterovich
Seconded: Danny Calegari, Peter Teichner
Authors
 Katrin Wehrheim Department of Mathematics Massachusetts Institute of Technology Cambridge, MA 02139 USA http://www-math.mit.edu/~katrin Chris T Woodward Department of Mathematics Rutgers University Piscataway, NJ 08854 USA http://www.math.rutgers.edu/~ctw