Related papers: Fukaya categories of hyperplane arrangements

We outline a proposal for a $2$-category $\mathrm{Fuet}_M$ associated to a hyperk\"ahler manifold $M$, which categorifies the subcategory of the Fukaya category of $M$ generated by complex Lagrangians. Morphisms in this $2$-category are…

We construct geometric maps from the cyclic homology groups of the (compact or wrapped) Fukaya category to the corresponding $S^1$-equivariant (Floer/quantum or symplectic) cohomology groups, which are natural with respect to all Gysin and…

We construct a version of Fourier transform for families of real tori. This transform defines a functor from certain category associated with a symplectic family of tori to the category of holomorphic vector bundles on the dual family (the…

Let $\mathfrak{Fuk}(T^*M)$ be the Fukaya category in the Fukaya's immersed Lagrangian Floer theory \cite{fukaya:immersed} which is generated by immersed Lagrangian submanifolds with clean self-intersections. This category is monoidal in…

We prove that homological mirror symmetry for very affine hypersurfaces respects certain natural symplectic operations (as functors between partially wrapped Fukaya categories), verifying conjectures of Auroux. These conjectures concern…

We introduce a new type of duality structure for $A_\infty$-categories called a relative weak Calabi-Yau pairing which generalizes Kontsevich and Soibelman's notion of a weak (proper) Calabi-Yau structure. We prove the existence of a…

For any high-dimensional Weinstein domain and finite collection of primes, we construct a Weinstein subdomain whose wrapped Fukaya category is a localization of the original wrapped Fukaya category away from the given primes. When the…

We study the Rouquier dimension of wrapped Fukaya categories of Liouville manifolds and pairs, and apply this invariant to various problems in algebraic and symplectic geometry. On the algebro-geometric side, we introduce a new method based…

Let $L$ be a monotone Lagrangian torus inside a compact symplectic manifold $X$, with superpotential $W_L$. We show that a geometrically-defined closed-open map induces a decomposition of the quantum cohomology $\operatorname{QH}^*(X)$ into…

We construct finite group actions on Lagrangian Floer theory when symplectic manifolds have finite group actions and Lagrangian submanifolds have induced group actions. We first define finite group actions on Novikov-Morse theory. We…

We construct a sheaf-theoretic analogue of the wrapped Fukaya category in Lagrangian Floer theory, by localizing a category of sheaves microsupported away from some given $\Lambda \subset S^*M$ along continuation maps constructed using the…

The main goal of this paper is to discuss a symplectic interpretation of Lipshitz, Ozsvath and Thurston's bordered Heegaard-Floer homology in terms of Fukaya categories of symmetric products and Lagrangian correspondences. More…

We construct the cyclic open--closed map for the big (i.e., bulk-deformed) relative Fukaya category, in the semipositive case, and show that it is a morphism of `polarized variations of semi-infinite Hodge structures'. We also give a…

We construct the $L_\infty$ structure on symplectic cohomology of a Liouville domain, together with an enhancement of the closed--open map to an $L_\infty$ homomorphism from symplectic cochains to Hochschild cochains on the wrapped Fukaya…

We prove homological mirror symmetry for projective hypersurfaces of sufficiently high degree using a functor from the wrapped Fukaya category of an affine hypersurface to the Fukaya category of its boundary at infinity.

We formulate some conjectures about the K-theory of symplectic manifolds and their Fukaya categories, and prove some of them in very special cases.

Let $L\subset X$ be a not necessarily orientable relatively $Pin$ Lagrangian submanifold in a symplectic manifold $X$. We construct a family of cyclic unital curved $A_\infty$ structures on differential forms on $L$ with values in the local…

We prove that every spherical object in the derived Fukaya category of a closed surface of genus at least two whose Chern character represents a non-zero Hochschild homology class is quasi-isomorphic to a simple closed curve equipped with a…

We provide a presymplectic characterization of Liouville sectors introduced by Ganatra-Pardon-Shende in terms of the characteristic foliation of the boundary, which we call Liouville $\sigma$-sectors. We extend this definition to the case…

We construct the Fukaya category of a closed surface equipped with an area form using only elementary (essentially combinatorial) methods. We also compute the Grothendieck group of its derived category.