We prove Tsyganâ€™s formality conjecture for Hochschild chains of the algebra of functions on an arbitrary smooth manifold M using the Fedosov resolutions proposed in math.QA/0307212 and the formalityâ€¦ (More)

The solution of Deligneâ€™s conjecture on Hochschild cochains and the formality of the operad of little disks provide us with a natural homotopy Gerstenhaber algebra structure on the Hochschildâ€¦ (More)

We give a proof of Kontsevichâ€™s formality theorem for a general manifold using Fedosov resolutions of algebras of polydifferential operators and polyvector fields. The main advantage of ourâ€¦ (More)

We consider a smooth Poisson affine variety with the trivial canonical bundle over C. For such a variety the deformation quantization algebra A~ enjoys the conditions of the Van den Bergh dualityâ€¦ (More)

We prove the additive version of the conjecture proposed by Ginzburg and Kaledin in [23]. This conjecture states that if X/G is an orbifold modeled on a quotient of a smooth affine symplectic varietyâ€¦ (More)

In this paper we prove Lie algebroid versions of Tsyganâ€™s formality conjecture for Hochschild chains both in the smooth and holomorphic settings. In the holomorphic setting our result implies aâ€¦ (More)

Proofs of Tsyganâ€™s formality conjectures for chains would unlock important algebraic tools which might lead to new generalizations of the Atiyah-Patodi-Singer index theorem and theâ€¦ (More)

In math.QA/0311303 B. Feigin, G. Felder, and B. Shoikhet proposed an explicit formula for the trace density map from the quantum algebra of functions on an arbitrary symplectic manifold M to the topâ€¦ (More)

A simple iterative procedure is suggested for the deformation quantization of (irregular) Poisson brackets associated to the classical Yang-Baxter equation. The construction is shown to admit a pureâ€¦ (More)

We present a classical r-matrix for the Hitchin system without marked points on an arbitrary non-degenerate algebraic curve of genus g â‰¥ 2 using Tyurin parameterization of holomorphic vector bundles.