Covariantly functorial wrapped Floer theory on Liouville sectors

Abstract

We introduce a class of Liouville manifolds with boundary which we call Liouville sectors. We define the wrapped Fukaya category, symplectic cohomology, and the open-closed map for Liouville sectors, and we show that these invariants are covariantly functorial with respect to inclusions of Liouville sectors. From this foundational setup, a local-to-global principle for Abouzaid's generation criterion follows.

arXiv commentFinal version to appear in Publ Math IHES, 115 pages, 15 figures

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Cited by in corpus (72)

• Geometric generation of the wrapped Fukaya category of Weinstein manifolds and sectors
• On partially wrapped Fukaya categories
• Microlocal Morse theory of wrapped Fukaya categories
• Bounds on spectral norms and barcodes
• The nonequivariant coherent-constructible correspondence for toric stacks
• Mirror symmetry for very affine hypersurfaces
• Floer theory and reduced cohomology on open manifolds
• Legendrian Weaves: N-graph Calculus, Flag Moduli and Applications
• Calabi-Yau structures on topological Fukaya categories
• The symplectic geometry of higher Auslander algebras: Symmetric products of disks
• Sheaf quantization in Weinstein symplectic manifolds
• Mayer-Vietoris property for relative symplectic cohomology
• Orlov and Viterbo functors in partially wrapped Fukaya categories
• Aspects of functoriality in homological mirror symmetry for toric varieties
• Tropical Lagrangian multi-sections and smoothing of locally free sheaves over degenerate Calabi-Yau surfaces
• Cyclic structures and broken cycles
• Homological mirror symmetry at large volume
• Mirror symmetry and Fukaya categories of singular hypersurfaces
• Lagrangian Skeleta of Hypersurfaces in $({\mathbb{C}}^{\ast }{)}^n$
• Generation for Lagrangian cobordisms in Weinstein manifolds
• Augmentations are sheaves for Legendrian graphs
• Continuous and coherent actions on wrapped Fukaya categories
• Smooth constructions of homotopy-coherent actions
• Prime-localized Weinstein subdomains
• Chekanov-Eliashberg dg-algebras for singular Legendrians
• Arboreal singularities from Lefschetz fibrations
• Sheaf Quantization of Legendrian Isotopy
• Mirror symmetry for Berglund-Hübsch Milnor fibers
• Simplicial descent for Chekanov-Eliashberg dg-algebras
• Holomorphic curves and continuation maps in Liouville bundles
• Mirror Symmetry for Truncated Cluster Varieties
• Wrapped sheaves
• Lagrangian Cobordisms in Liouville manifolds
• Representations, sheaves, and Legendrian $(2,m)$ torus links
• Selective symplectic homology with applications to contact non-squeezing
• The circle quantum group and the infinite root stack of a curve (with an appendix by Tatsuki Kuwagaki)
• Monodromy of monomially admissible Fukaya-Seidel categories mirror to toric varieties
• Mirror symmetry for honeycombs
• Positive arborealization of polarized Weinstein manifolds
• Projective twists and the Hopf correspondence
• Geometry and analysis of contact instantons and entanglement of Legendrian links I
• A Chekanov-Eliashberg algebra for Legendrian graphs
• b-Contact Structures on Tentacular Hyperboloids
• Homological mirror symmetry for elliptic Hopf surfaces
• Gamma II for toric varieties from integrals on T-dual branes and homological mirror symmetry
• Knot Categorification from Mirror Symmetry, Part II: Lagrangians
• Homological mirror symmetry for hypersurfaces in $({\mathbb{C}}^{\ast }{)}^n$
• Local mirror symmetry via SYZ
• Distinguishing open symplectic mapping tori via their wrapped Fukaya categories
• Lagrangian multi-sections and their toric equivariant mirror
• Secondary products in supersymmetric field theory
• Homological mirror symmetry for hypertoric varieties II (with an Appendix written jointly with Laurent Côté and Justin Hilburn)
• Computing the Rabinowitz Floer homology of tentacular hyperboloids
• Tangle contact homology
• Homological mirror symmetry for functors between Fukaya categories of very affine hypersurfaces
• Legendrian contact homology for attaching links in higher dimensional subcritical Weinstein manifolds
• Exotic families of symplectic manifolds with Milnor fibers of $ADE$-type
• Singular Legendrian unknot links and relative Ginzburg algebras
• Representing the big tilting sheaves as holomorphic Morse branes
• Symplectomorphisms and spherical objects in the conifold smoothing
• Smoothing, scattering, and a conjecture of Fukaya
• Variation of GIT and Variation of Lagrangian Skeletons I: Flip and Flop
• Categorical non-properness in wrapped Floer theory
• Microsheaves from Hitchin fibers via Floer theory
• SYZ for index 1 Fano hypersurfaces in projective space
• The infinity-category of stabilized Liouville sectors
• Symplectomorphisms of some Weinstein 4-manifolds
• A-infinity category of Lagrangian cobordisms in the symplectization of PxR
• Mapping tori of $A_{\infty }$-autoequivalences and Legendrian lifts of exact Lagrangians in circular contactizations
• An example of higher-dimensional Heegaard Floer homology
• Persistence of unknottedness of clean Lagrangian intersections
• Homological Mirror Symmetry for the universal centralizers I: The adjoint group case