Functors of wrapped Fukaya categories from Lagrangian correspondences

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.

v2; minor grammatical changes made for precision, proof of Proposition 7.19 rewritten in more details, Remark 7.32 added to properly clarify the relevant result of S. Ganatra's thesis [Gan13] that is cited

References in corpus (3)

• Technical details on Kuranishi structure and virtual fundamental chain
• Wrapped Floer cohomology and Lagrangian correspondences
• $SO(3)$-Floer homology of 3-manifolds with boundary 1

Cited by in corpus (8)

• Covariantly functorial wrapped Floer theory on Liouville sectors
• Geometric generation of the wrapped Fukaya category of Weinstein manifolds and sectors
• Homological mirror symmetry for Milnor fibers of simple singularities
• Intrinsic mirror symmetry and categorical crepant resolutions
• Projective twists and the Hopf correspondence
• Categorical non-properness in wrapped Floer theory
• Duality and kernels in microlocal geometry
• Lagrangian correspondences and the generalized Viterbo restriction functor