On partially wrapped Fukaya categories

Abstract

We define a new class of symplectic objects called "stops", which roughly speaking are Liouville hypersurfaces in the boundary of a Liouville domain. Locally, these can be viewed as pages of a compatible open book. To a Liouville domain with a collection of disjoint stops, we assign an $A_{\infty }$-category called its partially wrapped Fukaya category. An exact Landau-Ginzburg model gives rise to a stop, and the corresponding partially wrapped Fukaya category is meant to agree with the Fukaya category one is supposed to assign to the Landau-Ginzburg model. As evidence, we prove a formula that relates these partially wrapped Fukaya categories to the wrapped Fukaya category of the underlying Liouville domain. This operation is mirror to removing a divisor. In v2, we also construct continuation functors without cascades, which should be of independent interest.

arXiv commentv3: version accepted by the Journal of Topology. Some of the more routine proofs have been omitted

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• Perverse sheaves of categories and some applications
• Mirror symmetry and Fukaya categories of singular hypersurfaces
• Prime-localized Weinstein subdomains
• Mirror symmetry for Berglund-Hübsch Milnor fibers
• Simplicial descent for Chekanov-Eliashberg dg-algebras
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• Selective symplectic homology with applications to contact non-squeezing
• Lagrangian Cobordisms in Liouville manifolds
• Homological mirror symmetry for hypersurfaces in $({\mathbb{C}}^{\ast }{)}^n$
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• Homological mirror symmetry for functors between Fukaya categories of very affine hypersurfaces
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• A comparison of categorical and topological entropies on Weinstein manifolds
• Variation of GIT and Variation of Lagrangian Skeletons I: Flip and Flop
• An example of higher-dimensional Heegaard Floer homology
• Symplectomorphisms of some Weinstein 4-manifolds
• Persistence of unknottedness of clean Lagrangian intersections