A Formality Theorem for Hochschild Chains

Details A Formality Theorem for Hochschild Chains A Formality Theorem for Hochschild Chains

2004-02-16

arxiv.org/abs/math/0402248v4

Mathematics

Quantum Algebra

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

Scientific paper

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[[y_1, ..., 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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