相关论文: Simplicial descent for Chekanov-Eliashberg dg-alge…

The Chekanov-Eliashberg dg-algebra is a holomorphic curve invariant associated to Legendrian submanifolds of a contact manifold. We extend the definition to Legendrian embeddings of skeleta of Weinstein manifolds. Via Legendrian surgery,…

The Chekanov-Eliashberg dg-algebra is an algebraic invariant of Legendrian submanifolds of contact manifolds, whose definition recently has been extended to singular Legendrians. We describe a way of constructing simpler models of this…

We give the construction of the universal, natural up to homotopy Chern-Weil differential graded algebra homomorphism: $$cw: \mathcal{I} (G) \to \Omega ^{\bullet } (BG, \mathbb{R})$$ for infinite dimensional Milnor regular Lie groups $G$,…

Let $(\mathcal{C}, \otimes)$ be a monoidal dg-category. We construct a complex controlling the deformation of the monoidal structure on $\mathcal{C}$ together with the deformation of the underlying dg-category itself. We show that in the…

We provide a complete geometric solution to the problem of differentiating simplicial manifolds, extending classical Lie theory and complementing existing homotopical and formal approaches within a unifying framework. First, we establish a…

We associate to a quiver and a subquiver $(Q,F)$ a stopped Weinstein manifold $X$ whose Legendrian attaching link is a singular Legendrian unknot link $\varLambda$. We prove that the relative Ginzburg algebra of $(Q,F)$ is quasi-isomorphic…

In this note we realize the sheaf of Cherednik algebras $H_{1, c, X, G}$ on a general good complex orbifold $X/G$, originally introduced by Etingof for smooth complex varieties with an action by a finite group, by gluing sheaves of flat…

Let $L \subset Y$ be a Legendrian submanifold of a contact manifold, $S\subset L$ a framed embedded sphere bounding an isotropic disc $D_S \subset Y \setminus L$, and use $L_S$ to denote the manifold obtained from $L$ by a surgery on $S$.…

A pair $(K,K')$ consisting of a smooth triangulation $K$ of a compact smooth oriented Riemannian manifold $M$ and a sufficiently fine subdivision $K'$ determines a finite-dimensional Cheeger--Simons model $\mathscr{CS}(K,K')$ built from…

The Weinstein equation with complex coefficients is the equation governing generalized axisymmetric potentials (GASP) which can be written as $L_m[u]=\Delta u+\left(m/x\right)\partial_x u =0$, where $m\in\mathbb{C}$. We generalize results…

For the field $\mathbb{K} = \mathbb{R}$ or $\mathbb{C}$, and an integrable distribution $F \subseteq T_M \otimes_{\mathbb{R}} \mathbb{K}$ on a smooth manifold $M$, we study the Hochschild cohomology of the dg manifold $(F[1],d_F)$ and…

The purpose of this article is to investigate relations between W-superalgebras and integrable super-Hamiltonian systems. To this end, we introduce the generalized Drinfel'd-Sokolov (D-S) reduction associated to a Lie superalgebra $g$ and…

In this paper we study the descent problem of cohesive modules on complex manifolds. For a complex manifold $X$ we could consider the Dolbeault dg-algebra $\mathcal{A}(X)$ on it and Block in 2006 introduced a dg-category…

This is the first of a series of two articles aiming at relating the compact Fukaya category of a Weinstein manifold to the derived category of finite dimensional representations of the Chekanov-Eliashberg differential graded algebra of the…

Let $\Sigma_g$ be a closed Riemann surface of genus $g$. Let $G$ be a finite subgroup of the automorphism group of $\Sigma_g$. It is well known that there exists a smooth $G$-equivariant embedding from $\Sigma_g$ to some Euclidean space…

In this article we study the perverse sheaf on Drinfeld's compactification obtained by applying the geometric Jacquet functor (alias nearby cycles) to a nondegenerate Whittaker sheaf. Namely, we describe its restrictions along the defect…

We discuss the `hd-compactification' of a semi-simple Lie group to a manifold with corners; it is the real analog of the wonderful compactification of deConcini and Procesi. There is a 1-1 correspondence between the boundary faces of the…

To any non-negatively graded dg Lie algebra $g$ over a field $k$ of characteristic zero we assign a functor $\Sigma_g: art/k \to Kan$ from the category of commutative local artinian $k$-algebras with the residue field $k$ to the category of…

The category of unital (unbounded) dg cocommutative coalgebras over a field of characteristic zero is provided with a structure of simplicial closed model category. This generalizes the model structure defined by Quillen in 1969 for…

We derive explicit formulas for lambda-brackets of the affine classical W-algebras attached to the minimal and short nilpotent elements of any simple Lie algebra g. This is used to compute explicitly the first non-trivial PDE of the…