On the Hochschild-Kostant-Rosenberg map for graded manifolds

Abstract

We show that the Hochschild-Kostant-Rosenberg map from the space of multivector fields on a graded manifold N (endowed with a Berezinian volume) to the cohomology of the algebra of multidifferential operators on N (as a subalgebra of the Hochschild complex of the algebra of smooth functions on N) is an isomorphism of Batalin-Vilkovisky algebras. These results generalize to differential graded manifolds.

15 pages. Problematic Lemma 5.5 of v1 removed and Theorem 5.3b corrected accordingly. Exposition reorganized. To appear in IMRN

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• Hochschild cohomology of dg manifolds associated to integrable distributions
• From topological field theory to deformation quantization and reduction