Related papers: A Proof of Tsygan's Formality Conjecture for an Ar…
We prove Tsygan'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 formality quasi-isomorphism for Hochschild chains…
In this paper we prove Lie algebroid versions of Tsygan's formality conjecture for Hochschild chains both in the smooth and holomorphic settings. In the holomorphic setting our result implies a version of Tsygan's formality conjecture for…
We prove a conjecture raised by Tsygan, namely the existence of an L-infinity-quasiisomorphism of L-infinity-modules between the cyclic chain complex of smooth functions on a manifold and the differential forms on that manifold. Concretely,…
In this paper we complete the proof of Caldararu's conjecture on the compatibility between the module structures on differential forms over poly-vector fields and on Hochschild homology over Hochschild cohomology. In fact we show that…
In this short note we prove an equivariant version of the formality of multidiffirential operators for a proper Lie group action. More precisely, we show that the equivariant Hochschild-Kostant-Rosenberg quasi-isomorphism between the…
In this paper we prove, with details and in full generality, that the isomorphism induced on tangent homology by the Shoikhet-Tsygan formality $L_\infty$-quasi-isomorphism for Hochschild chains is compatible with cap-products. This is a…
It is believed arXiv:0808.2762, arXiv:math/9904055 that, among the coefficients entering Kontsevich's formality quasi-isomorphism arXiv:q-alg/9709040, there are irrational (possibly even transcendental) numbers. In this paper, we prove that…
We give a proof of Kontsevich's formality theorem for a general manifold using Fedosov resolutions of algebras of polydifferential operators and polyvector fields. The main advantage of our construction of the formality quasi-isomorphism is…
We develop a formalism involving Atiyah classes of sheaves on a smooth manifold, Hochschild chain and cochain complexes. As an application we prove a version of the Riemann--Roch theorem.
We extend the Kontsevich formality $L_\infty$-morphism $\U\colon T^\ndot_\poly(\R^d)\to\D^\ndot_\poly(\R^d)$ to an $L_\infty$-morphism of an $L_\infty$-modules over $T^\ndot_\poly(\R^d)$, $\hat \U\colon C_\ndot(A,A)\to\Omega^\ndot(\R^d)$,…
We prove the formality theorem for the differential graded Lie algebra module of Hochschild chains for the algebra of endomorphisms of a smooth vector bundle. We discuss a possible application of this result to a version of the algebraic…
The formal algebraic structures that govern higher-spin theories within the unfolded approach turn out to be related to an extension of the Kontsevich Formality, namely, the Shoikhet-Tsygan Formality. Effectively, this allows one to…
The formality theorem for Hochschild chains of the algebra of functions on a smooth manifold gives us a version of the trace density map from the zeroth Hochschild homology of a deformation quantization algebra to the zeroth Poisson…
The solution of Deligne'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 Hochschild cochains of an associative algebra. In this…
In this short note we describe an alternative global version of the twisting procedure used by Dolgushev to prove formality theorems. This allows us to describe the maps of Fedosov resolutions, which are key factors of the formality…
It is proved that the associative differential graded algebra of (polynomial) polyvector fields on a vector space (may be infinite- dimensional) is quasi-isomorphic to the corresponding cohomological Hochschild complex of (polynomial)…
We show how a novel construction of the sheaf of Cherednik algebras on a quotient orbifold Y=X/G by virtue of formal geometry in author's prior work leads to results for the sheaf of Cherednik algebra which until recently were viewed as…
The Kontsevich-Soibelman solution of the cyclic version of Deligne's conjecture and the formality of the operad of little discs on a cylinder provide us with a natural homotopy calculus structure on the pair (C^*(A), C_*(A)) ``Hochschild…
On a flat manifold, M. Kontsevich's formality quasi-isomorphism is compatible with cup-products on tangent cohomology spaces, in the sense that its derivative at any formal Poisson 2-tensor induces an isomorphism of graded commutative…
The Tamarkin Tsygan calculus of a finite dimensional algebra is a differential calculus given by the comprehensive data of the Hochschild cohomology, its structure both as a graded commutative algebra under the cup product and as a graded…