Functors of wrapped Fukaya categories from Lagrangian correspondences

2017/12/01 by Yuan Gao, Gao, Yuan · 3 citations
Mathematics · #53D37 #53D40 #Algebraic structures and combinatorial models #FOS: Mathematics #Geometric and Algebraic Topology #Homotopy and Cohomology in Algebraic Topology #Symplectic Geometry (math.SG)

paper · pdf · doi:10.48550/arxiv.1712.00225

openalex publication_date 2017/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We study wrapped Floer theory on product Liouville manifolds and prove that the wrapped Fukaya categories defined with respect to two different kinds of natural Hamiltonians and almost complex structures are equivalent. The implication is we can do quilted version of wrapped Floer theory, based on which we then construct functors between wrapped Fukaya categories of Liouville manifolds from certain classes of Lagrangian correspondences, by enlarging the wrapped Fukaya categories appropriately, allowing exact cylindrical Lagrangian immersions. For applications, we present a general Künneth formula, and also identify the Viterbo restriction functor with the functor associated to the completed graph of embedding of a Liouville sub-domain.

Citations

• Orientations for pseudoholomorphic quilts

Cited by

• Proper kernels in microlocal sheaf theory
• Generation of immersed Lagrangians by cocores
• Homological mirror symmetry for Milnor fibers of simple singularities

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• Wrapped Floer cohomology and Lagrangian correspondences
• Lagrangian correspondences and the generalized Viterbo restriction functor
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