Quilted Floer cohomology

Wehrheim, Katrin¹ ; Woodward, Chris T²

¹ Department of Mathematics, Massachusetts Institute of Technology, Cambridge, MA 02139, USA
² Department of Mathematics, Rutgers University, Piscataway, NJ 08854, USA

Geometry & topology, Tome 14 (2010) no. 2, pp. 833-902.

Résumé

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.

Détail

DOI : 10.2140/gt.2010.14.833

Keywords: Floer theory, Lagrangian correspondence, Hamiltonian nondisplaceability

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