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Lagrangian Cobordism and Fukaya Categories (1304.6032v3)
Published 22 Apr 2013 in math.SG and math.GT
Abstract: Given a symplectic manifold M, we consider a category with objects finite ordered families of Lagrangian submanifolds of M (subject to certain additional constraints) and with morphisms Lagrangian cobordisms relating them. We construct a functor that maps this category to a variant of the derived Fukaya category of M in a way that takes into account the triangulated structure of the latter.