Abstract

The existence of star products on any Poisson manifold M is a consequence of Kontsevich’s formality theorem, the proof of which is based on an explicit formula giving a formality quasi-isomorphism in the flat case M = R^d. We propose here a coherent choice of orientations and signs in order to carry on Kontsevich’s proof in the R^d case, i.e., prove that Kontsevich’s formality quasi-isomorphism verifies indeed the formality equation with all the signs precised.

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