Related papers: Fedosov connections on jet bundles and deformation…
This paper review one construction of Frobenius manifolds (and slightly weaker structures). It splits it into several steps and discusses the freedom and the constraints in these steps. The steps pass through holomorphic bundles with…
We extend the author's and CPTVV's correspondence between shifted symplectic and Poisson structures to establish a correspondence between exact shifted symplectic structures and non-degenerate shifted Poisson structures with formal…
It is shown that a (curved) projective structure on a smooth manifold determines on the Poisson algebra of smooth, fiberwise-polynomial functions on the cotangent bundle a one-parameter family of graded star products. For a particular value…
Motivated by the study of symplectic Lie algebroids, we study a describe a type of algebroid (called an $E$-tangent bundle) which is particularly well-suited to study of singular differential forms and their cohomology. This setting…
We study basic properties of supermanifolds endowed with an even (odd) symplectic structure and a connection respecting this symplectic structure. Such supermanifolds can be considered as generalization of Fedosov manifolds to the…
We introduce the notion of asymptotically finitely generated contact structures, which states essentially that the Symplectic Homology in a certain degree of any filling of such contact manifolds is uniformly generated by only finitely many…
One defines the notion of universal deformation quantization: given any manifold $M$, any Poisson structure $\P$ on $M$ and any torsionfree linear connection $\nabla$ on $M$, a universal deformation quantization associates to this data a…
We study the relations between the projective and the almost conformally symplectic structures on a smooth even dimensional manifold. We describe these relations by a single almost conformally symplectic connection with totally trace--free…
We investigate orthogonal and symplectic bundles with parabolic structure, over a curve.
In earlier work (*) we studied an extension of the canonical symplectic structure in the cotangent bundle of an affine space ${\cal Q}={\bf R}^N$, by additional terms implying the Poisson non-commutativity of both configuration and momentum…
We present a method of quantizing analytic spaces $X$ immersed in an arbitrary smooth ambient manifold $M$. Remarkably our approach can be applied to singular spaces. We begin by quantizing the cotangent bundle of the manifold $M$. Using a…
Star products on the classical double group of a simple Lie group and on corresponding symplectic grupoids are given so that the quantum double and the "quantized tangent bundle" are obtained in the deformation description. "Complex"…
Fix a stable degree-$n$ rank-$k$ bundle $\mathcal{F}$ on a complex elliptic curve for (coprime) $1\le k<n\ge 3$. We identify the symplectic leaves of the Poisson structure introduced independently by Polishchuk and Feigin-Odesskii on…
We investigate a two-cocycle on the group of symplectic diffeomorphisms of an exact symplectic manifolds defined by Ismagilov, Losik, and Michor and investigate its properties. We provide both vanishing and non-vanishing results and…
We prove the uniqueness, up to diffeomorphism, of symplectically aspherical fillings of the unit cotangent bundle of odd-dimensional spheres. As applications, we first show the non-existence of exact symplectic cobordisms between some…
We observe that numerous symplectic resolutions can be expressed as intersections of twisted cotangent bundles. Additionally, their dual symplectic resolutions can be derived from intersections of dual twisted cotangent bundles. We…
In a non-compact setting, the notion of hyperbolicity, and the associated structure of stable and unstable manifolds (for unbounded orbits), is highly dependent on the choice of metric used to define it. We consider the simplest version of…
In this article we relate the construction of Ricci type symplectic connections by reduction to the construction of star product by reduction yielding rather explicit descriptions for the star product on the reduced space.
This is a report on recent progress concerning the interactions between derived algebraic geometry and deformation quantization. We present the notion of derived algebraic stacks, of shifted symplectic and Poisson structures, as well as the…
The paper is devoted to study of Massey products in symplectic manifolds. Theory of generalized and classical Massey products and a general construction of symplectic manifolds with nontrivial Massey products of arbitrary large order are…