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math.DG2000
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…
math.KT2000
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…
math.KT2000
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.