Morita equivalence and characteristic classes of star products

This paper deals with two aspects of the theory of characteristic classes of star products: first, on an arbitrary Poisson manifold, we describe Morita equivalent star products in terms of their Kontsevich classes; second, on symplectic manifolds, we describe the relationship between Kontsevich’s and Fedosov’s characteristic classes of star products.

💡 Research Summary

The paper addresses two intertwined problems in deformation quantization: (i) a complete description of Morita‑equivalent star products on an arbitrary Poisson manifold in terms of their Kontsevich characteristic classes, and (ii) an explicit comparison between Kontsevich’s and Fedosov’s characteristic classes on symplectic manifolds.

The first part begins by recalling Kontsevich’s formality theorem, which associates to any formal Poisson bivector (\pi_\hbar) a star product (*) and a cohomology class (