A Formality Theorem for Hochschild Chains

2004/02/16 by Vasiliy Dolgushev, Dolgushev, Vasiliy
Mathematics · Physics and Astronomy · #Advanced Topics in Algebra #Algebraic structures and combinatorial models #Homotopy and Cohomology in Algebraic Topology #hep-th #math.DG #math.KT #math.QA #msc:16E45 #msc:18G55 #msc:53C15

paper · pdf · doi:10.48550/arxiv.math/0402248

41 pages, 5 figures. To appear in Adv. Math

arxiv created 2004/10/25 · arxiv updated 2009/12/01

Abstract

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 of R[[y₁, ..., y_d]] proposed in paper math.QA/0010321 by Shoikhet. This result allows us to describe traces on the quantum algebra of functions on an arbitrary Poisson manifold.

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