A Formality Theorem for Hochschild Chains

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[[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.

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

References in corpus (7)

• Deformation quantization of Poisson manifolds, I
• Introduction to sh Lie algebras for physicists
• Target space symmetries in topological theories I
• On the Globalization of Kontsevich's Star Product and the Perturbative Poisson Sigma Model
• Formality conjecture for chains
• Riemann-Roch-Hirzebruch theorem and Topological Quantum Mechanics
• On the cyclic Formality conjecture