Related papers: Distinguishing open symplectic mapping tori via th…

We develop a purely categorical theory of action filtrations and their associated growth invariants. When specialized to categories of geometric interest, such as the wrapped Fukaya category of a Weinstein manifold, and the bounded derived…

A class of partially wrapped Fukaya categories in $T^* N$ are proven to be well defined and then studied. In the case of $N$ diffeomorphic to $\mathbb{R}^m \times \mathbb{T}^n$, it is shown that these categories provide homological mirrors…

In this paper, motivated by symplectic topology, we explore categorical entropy and present two main results. The first result establishes a relation between categorical entropies of functors on a category and its localization.…

We build the wrapped Fukaya category W(E) for any monotone symplectic manifold, convex at infinity. We define the open-closed and closed open-string maps. We study their algebraic properties and prove that the string maps are compatible…

Given a monotone Lagrangian $L$ in a compact symplectic manifold $X$, we construct a commutative diagram relating the closed-open string map $\mathcal{CO}_\lambda \colon \operatorname{QH}^*(X) \to \operatorname{HH}^*(\mathcal{F}…

We prove that a Weinstein domain symplectically embedded in a closed symplectic manifold always admits symplectic hypersurfaces in its complement, possibly after a deformation. As a consequence, we obtain an obstruction for a closed…

We derive constraints on Lagrangian embeddings in completions of certain stable symplectic fillings with semisimple symplectic cohomologies. Manifolds with these properties can be constructed by generalizing the boundary connected sum…

We study families of objects in Fukaya categories, specifically ones whose deformation behaviour is prescribed by the choice of an odd degree cohomology class. This leads to invariants of symplectic manifolds, which we apply to blowups…

In this paper we construct, in all odd complex dimensions, pairs of Liouville domains W_0 and W_1 which are diffeomorphic to the cotangent bundle of the sphere with one extra subcritical handle, but are not symplectomorphic. While W_0 is…

Homological mirror symmetry (HMS) asserts that the Fukaya category of a symplectic manifold is derived equivalent to the category of coherent sheaves on the mirror complex manifold. Without suitable enlargement (split closure) of the Fukaya…

We study two functors between (partially) wrapped Fukaya categories. The first is the Orlov functor from the Fukaya category of a stop to the Fukaya category of the ambient sector. We give a geometric criterion for when this functor is…

Given a Hamiltonian torus action on a symplectic manifold, Teleman and Fukaya have proposed that the Fukaya category of each symplectic quotient should be equivalent to an equivariant Fukaya category of the original manifold. We lay out new…

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…

To a conical symplectic resolution with Hamiltonian torus action, Braden--Proudfoot--Licata--Webster associate a category O, defined using deformation quantization (DQ) modules. It has long been expected, though not stated precisely in the…

Let $X$ denote the `conifold smoothing', the symplectic Weinstein manifold which is the complement of a smooth conic in $T^*S^3$, or equivalently the plumbing of two copies of $T^*S^3$ along a Hopf link. Let $Y$ denote the `conifold…

The Nadler--Zaslow correspondence famously identifies the finite-dimensional Floer homology groups between Lagrangians in cotangent bundles with the finite-dimensional Hom spaces between corresponding constructible sheaves. We generalize…

For a symplectic manifold satisfying some topological condition,we define a special class of modules over the deformation quantization algebra. For any two such modules we construct an infinity local system of morphisms. We construct such…

In this paper, using similar idea as in Fukaya-Oh's work ([9]), we devise a method to compute the Fukaya category of certain exact symplectic manifolds by reducing it to the corresponding Morse category of non-Hausdorff manifold as…

Let $Ham (M,\omega ) $ denote the Frechet Lie group of Hamiltonian symplectomorphisms of a monotone symplectic manifold $(M, \omega) $. Let $NFuk (M, \omega)$ be the $A _{\infty} $-nerve of the Fukaya category $Fuk (M, \omega)$, and let…

Given an exact relatively Pin Lagrangian embedding Q in a symplectic manifold M, we construct an A-infinity restriction functor from the wrapped Fukaya category of M to the category of modules on the differential graded algebra of chains…