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8 papers
Remarks on modules over deformation quantization algebras
Ryszard Nest, Boris Tsygan
We study an asymptotic version of the Maslov-Hormander construction of Lagrangian distributions in terms of deformation quantization.
Local formula for the index of a Fourier Integral Operator
Eric Leichtnam, Ryszard Nest, Boris Tsygan
We show that the index of an elliptic Fourier integral operator associated to a contact diffeomorphism of cosphere bundles of two Riemannian manifolds X and Y is given by $\int…
Noncommutative differential calculus, homotopy BV algebras and formality conjectures
Dmitri Tamarkin, Boris Tsygan
We define a notion of astrongly homotopy BV algebra and apply it to deformation theory problems. Formality conjectures for Hochschild and cyclic chains are formulated. We prove som…
Riemann-Roch via deformation quantization, II
Paul Bressler, Ryszard Nest, Boris Tsygan
We prove a Riemann-Roch formula for deformation quantization of complex manifolds and its corollary, an index theorem for elliptic pairs conjectured by Schapira and Schneiders.
Deformations of symplectic Lie algebroids, deformations of holomorphic symplectic structures, and index theorems
Ryszard Nest, Boris Tsygan
Recently Kontsevich solved the classification problem for deformation quantizations of all Poisson structures on a manifold. In this paper we study those Poisson structures for whi…
Formality conjecture for chains
Boris Tsygan
We state the analogs of Kontsevich's formality conjecture for Hochschild and cyclic chains, as well as their