Related papers: Multiple Derived Lagrangian Intersections

In this article, we study the question of existence of leafwise intersection points for contact manifolds which are not necessarily of restricted contact type. Moreover we can find a leafwise intersection point on the symplectization for…

We consider Lagrangian Floer cohomology for a pair of Lagrangian submanifolds in a symplectic manifold M. Suppose that M carries a symplectic involution, which preserves both submanifolds. Under various topological hypotheses, we prove a…

Hypergraphs extend traditional graphs by enabling the representation of N-ary relationships through higher-order edges. Akin to a common approach of deriving graph Laplacians, we define function spaces and corresponding symmetric products…

In this article, we modify the proof of holomorphic quilts from Wehrheim and Woodward in \cite{wehrheim2009floer} to construct a specific type of immersed holomorphic quilt, where the symplectic manifolds are closed surfaces. The…

Let $M$ be a smooth projective variety and $\mathbf{D}$ an ample normal crossings divisor. From topological data associated to the pair $(M, \mathbf{D})$, we construct, under assumptions on Gromov-Witten invariants, a series of…

We introduce a notion of coisotropics on 1-shifted symplectic Lie groupoids (i.e. quasi-symplectic groupoids) using twisted Dirac structures and show that it satisfies properties analogous to the corresponding derived-algebraic notion in…

Hamiltonian stationary Lagrangian submanifolds (HSLAG) are a natural generalization of special Lagrangian manifolds (SLAG). The latter only make sense on Calabi-Yau manifolds whereas the former are defined for any almost K\"ahler manifold.…

We study two related invariants of Lagrangian submanifolds in symplectic manifolds. For a Lagrangian torus these invariants are functions on the first cohomology of the torus. The first invariant is of topological nature and is related to…

We study piecewise linear knot diagrams in the base of almost toric fibrations of symplectic four-manifolds. These diagrams translate to deformations of the almost toric fibration. We give several applications to symplectic topology, among…

We use tropical curves and toric degeneration techniques to construct closed embedded Lagrangian rational homology spheres in a lot of Calabi-Yau threefolds. We apply this construction to the tropical curves obtained from the 2875 lines on…

Two smooth map germs are right-equivalent if and only if they generate two Lagrangian submanifolds in a cotangent bundle which have the same contact with the zero-section. In this paper we provide a reverse direction to this classical…

Generalizing work of Markushevich--Tikhomirov and Arbarello--Sacc\`a--Ferretti, we use relative Prym varieties to construct Lagrangian fibered symplectic varieties in infinitely many dimensions. We then give criteria for when the…

We give an intrinsic definition of toric symplectic stacks, and show that they are classified by simple convex polytopes equipped with some additional combinatorial data. This generalizes Delzant's classification of toric symplectic…

We introduce constructions of exact Lagrangian cobordisms with cylindrical Legendrian ends and study their invariants which arise from Symplectic Field Theory. A pair $(X,L)$ consisting of an exact symplectic manifold $X$ and an exact…

On a complex symplectic manifold, we construct the stack of quantization-deformation modules, that is, (twisted) modules of microdifferential operators with an extra central parameter, a substitute to the lack of homogeneity. We also…

We give finiteness results and some classifications up to diffeomorphism of minimal strong symplectic fillings of Seifert fibered spaces over S^2 satisfying certain conditions, with a fixed natural contact structure. In some cases we can…

We study the Lagrangian isotopy classification of Lagrangian spheres in the Milnor fibre, $B_{d,p,q}$, of the cyclic quotient surface T-singularity $\frac{1}{dp^2} (1,dpq-1)$. We prove that there is a finitely generated group of…

We construct using Lefschetz fibrations a large family of contact manifolds with the following properties: Any bounding contact embedding into an exact symplectic manifold satisfying a mild topological assumption is non-displaceable and…

The purpose of this paper is to present some results on the existence of homologous, nonisotopic symplectic or lagrangian surfaces embedded in a simply connected symplectic 4-dimensional manifold.

We continue our study of tempered oscillatory integrals $I_\varphi(a)$, here investigating the link with a suitable symplectic structure at infinity, which we describe in detail. We prove adapted versions of the classical theorems, which…