Functoriality for Lagrangian correspondences in Floer theory

Details Functoriality for Lagrangian correspondences in Floer theory Functoriality for Lagrangian correspondences in Floer theory

2007-08-21

arxiv.org/abs/0708.2851v3

Mathematics

Symplectic Geometry

minor corrections and updated references; original 120 page preprint got split into 4 parts - this is one of them

Scientific paper

Using quilted Floer cohomology and relative quilt invariants, we define a composition functor for categories of Lagrangian correspondences in monotone and exact symplectic Floer theory. We show that this functor agrees with geometric composition in the case that the composition is smooth and embedded. As a consequence we obtain 'categorification commutes with composition' for Lagrangian correspondences.

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