Related papers: On Fukaya categories and prequantization bundles

The Dolbeault resolution of the sheaf of holomorphic vector fields $Lie$ on a complex manifold $M$ relates $Lie$ to a sheaf of differential graded Lie algebras, known as the Fr\"olicher-Nijenhuis algebra $g$. We establish - following B. L.…

We prove that Lagrangian cocores and Lagrangian linking disks of a stopped Weinstein manifold generate the Lagrangian cobordism infinity-category. As a geometric consequence, we see that any brane (after stabilization) admits a Lagrangian…

We analyse holomorphic discs on Lagrangian SU(2)-orbits in a family of quasihomogeneous threefolds of SL(2, C), previously studied by Evans-Lekili, introducing several techniques that should be applicable to wider classes of homogeneous…

This paper is about the Fukaya category of a Fano hypersurface $X \subset \mathbb{CP}^n$. Because these symplectic manifolds are monotone, both the analysis and the algebra involved in the definition of the Fukaya category simplify…

We prove the Novikov conjecture on oriented Cheeger spaces whose fundamental group satisfies the strong Novikov conjecture. A Cheeger space is a stratified pseudomanifold admitting, through a choice of ideal boundary conditions, an L2-de…

Consider a pair $(X,L)$, of a Weinstein manifold $X$ with an exact Lagrangian submanifold $L$, with ideal contact boundary $(Y,\Lambda)$, where $Y$ is a contact manifold and $\Lambda\subset Y$ is a Legendrian submanifold. We introduce the…

The weight $\theta$-sheaf $\underline{\mathbb{R}}_{X,\theta}$ helps us to reinterpret Morse-Novikov cohomologies via sheaf theory. We give several theorems of K\"{u}nneth and Leray-Hirsch types. As applications, we prove that the…

In this paper, we construct a Fukaya category of any infinite type surface whose objects are gradient sectorial Lagrangians. This class of Lagrangian submanifolds is introduced by one of the authors in [Oh21b] which can serve as an object…

Here we study several questions concerning Liouville domains that are diffeomorphic to cylinders, so called trivial bi-fillings, for which the Liouville skeleton moreover is smooth and of codimension one; we also propose the notion of a…

The action of the total cohomology $H^*(M)$ of the almost Kahler manifold $M$ on its Floer cohomology, int roduced originally by Floer, gives a new ring structure on $H^*(M)$. We prove that the total cohomology space $H^* (M)$, provided…

We establish an infinitesimal version of fragility for squared Dehn twists around even dimensional Lagrangian spheres. The precise formulation involves twisting the Fukaya category by a closed two-form or bulk deforming it by a…

We build a bridge between Floer theory on open symplectic manifolds and the enumerative geometry of holomorphic disks inside their Fano compactifications, by detecting elements in symplectic cohomology which are mirror to Landau-Ginzburg…

We embed triangulated categories defined by quivers with potential arising from ideal triangulations of marked bordered surfaces into Fukaya categories of quasi-projective 3-folds associated to meromorphic quadratic differentials. Together…

We study the Lagrangian quantum homology of real parts of Fano toric manifolds of minimal Chern number at least 2, using coefficients in a ring of Laurent polynomials over Z/2Z. We show that these Lagrangians are wide, in the sense that…

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 describe the (bigraded) Hochschild cohomology of graded gentle algebras along with the Gerstenhaber bracket and cup product. In particular, this yields a description of the Hochschild cohomology of partially wrapped Fukaya categories of…

Certain quantization problems are equivalent to the construction of morphisms from "quantum" to "classical" props. Once such a morphism is constructed, Hensel's lemma shows that it is in fact an isomorphism. This gives a new, simple proof…

We construct a Lagrangian in the cotangent bundle of a 3-torus whose projection to the fiber is a neighborhood of a tropical curve with a single 4-valent vertex. This Lagrangian has an isolated conical singular point, and its smooth locus…

Fukaya categories are deep and rich invariants of symplectic manifolds which are notoriously difficult to compute explicitly. In the case of surfaces, however, the situation is simple, combinatorial,and is very well understood (at least by…

In this paper, we translate the Springer theory of Weyl group representations into the language of symplectic topology. Given a semisimple complex group G, we describe a Lagrangian brane in the cotangent bundle of the adjoint quotient g/G…