Related papers: Koszul duality patterns in Floer theory

Given a closed oriented surface $\Sigma$ of genus greater than 0, we construct a map $\mathcal{F}$ from the higher-dimensional Heegaard Floer homology of the cotangent fibers of $T^*\Sigma$ to the Hecke algebra associated to $\Sigma$ and…

We relate the version of rational Symplectic Field Theory for exact Lagrangian cobordisms introduced in [5] with linearized Legendrian contact homology. More precisely, if $L\subset X$ is an exact Lagrangian submanifold of an exact…

Let $\Gamma$ be a minimal connected negative-definite plumbing tree with all vertices of genus zero, and let $Y_\Gamma$ be the oriented link of the corresponding normal complex surface singularity, equipped with its canonical contact…

For each positive integer n, Khovanov and Rozansky constructed an invariant of links in the form of a doubly-graded cohomology theory whose Euler characteristic is the sl(n) link polynomial. We use Lagrangian Floer cohomology on some…

We discuss D-branes of the topological A-model (A-branes), which are believed to be closely related to the Fukaya category. We give string theory arguments which show that A-branes are not necessarily Lagrangian submanifolds in the…

Let $X$ be a compact toric variety. The quantum cohomology of $X$ decomposes as a direct sum, and associated to each summand $Q$ is a toric fibre $L_Q$ with rank $1$ local system. By building an explicit twisted-complex-like object, we show…

We introduce a contravariant functor, called Floer functor, from the category of Lagrangian conductors of a symplectic manifold to the homotopy category of bounded chain complexes of open strings in this manifold. The latter two categories…

This paper introduces the category of marked curved Lie algebras with curved morphisms, equipping it with a closed model category structure. This model structure is---when working over an algebraically closed field of characteristic…

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 $M$ be a triangulated oriented closed connected manifold with universal cover $\widetilde{M}\to M$ and fundamental group $\Gamma=\pi_1(M)$ and consider an essentially free measure preserving action $\Gamma\curvearrowright (X,\mu)$ on a…

In mirror symmetry, symplectic Landau-Ginzburg models are mirror to a large class of examples, in particular to Fano varieties and hypersurfaces of many Calabi-Yau and Fano varieties. When studying their Fukaya categories on the A-model in…

Mirror symmetry for higher genus curves is usually formulated and studied in terms of Landau-Ginzburg models; however the critical locus of the superpotential is arguably of greater intrinsic relevance to mirror symmetry than the whole…

We develop the gluing theory of contact instantons in the context of open strings and in the context of closed strings \emph{with vanishing charge}, for example in the symplectization context. This is one of the key ingredients for the…

We prove that the wrapped Fukaya category of a punctured sphere ($S^2$ with an arbitrary number of points removed) is equivalent to the triangulated category of singularities of a mirror Landau-Ginzburg model, proving one side of the…

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…

This paper investigates the representation-theoretic structure of the Koszul cohomology of a smooth projective variety $X$ over an algebraically closed field $k$, admitting an action of a finite group $G$ of order coprime to ${\rm…

We prove that the inclusion of every closed exact Lagrangian with vanishing Maslov class in a cotangent bundle is a homotopy equivalence. We start by adapting an idea of Fukaya-Seidel-Smith to prove that such a Lagrangian is equivalent to…

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 study several notions of dimension for (pre-)triangulated categories naturally arising from topology and symplectic geometry. We prove new bounds on these dimensions and raise several questions for further investigation. For instance, we…

Let X be a smooth toric variety defined by the fan {\Sigma} . We consider {\Sigma} as a finite set with topology and define a natural sheaf of graded algebras A_{\Sigma} on {\Sigma} . The category of modules over A_{\Sigma} is studied…