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Functoriality for Lagrangian correspondences in Floer theory

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arxiv 0708.2851 v3 pith:IOY6LATJ submitted 2007-08-21 math.SG math.DG

Katrin Wehrheim , Chris T. Woodward This is my paper · ORCID
classification math.SGmath.DG
keywords compositioncorrespondencesfloerlagrangianfunctortheoryagreescase
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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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  1. The Dual DG Category to Weinstein's symplectic "category" and applications to Geometric Quantization

    math.SG 2026-08 conditional novelty 7.0 of 10

    A true differential graded category dual to Weinstein's symplectic category is constructed from prequantum systems, with an osp(1|2) superalgebra action and a vanishing theorem relating its cohomology to holomorphic q...

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