Volume 14, issue 2 (2010)

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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
Mathematical Subject Classification 2000
Primary: 53D40
Secondary: 57R56
References
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