51 citations · 230 across the 22 of their papers we have counts for
22 papers
Morita equivalence and characteristic classes of star products
H. Bursztyn, V. Dolgushev, S. Waldmann
This paper deals with two aspects of the theory of characteristic classes of star products: first, on an arbitrary Poisson manifold, we describe Morita equivalent star products in…
Proof of Swiss Cheese Version of Deligne's Conjecture
Vasiliy Dolgushev, Dmitry Tamarkin, Boris Tsygan
For an associative algebra A we consider the pair "the Hochschild cochain complex C*(A,A) and the algebra A". There is a natural 2-colored operad which acts on this pair. We show t…
Noncommutative calculus and the Gauss-Manin connection
V. Dolgushev, D. Tamarkin, B. Tsygan
After an overview of noncommutative differential calculus, we construct parts of it explicitly and explain why this construction agrees with a fuller version obtained from the theo…
Formality theorems for Hochschild complexes and their applications
V. A. Dolgushev, D. E. Tamarkin, B. L. Tsygan
We give a popular introduction to formality theorems for Hochschild complexes and their applications. We review some of the recent results and prove that the truncated Hochschild c…
Formality of the homotopy calculus algebra of Hochschild (co)chains
Vasiliy Dolgushev, Dmitry Tamarkin, Boris Tsygan
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 cal…
An algebraic index theorem for Poisson manifolds
V. A. Dolgushev, V. N. Rubtsov
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 de…