# On the Hochschild-Kostant-Rosenberg map for graded manifolds

Cattaneo, A S; Fiorenza, D; Longoni, R (2005). On the Hochschild-Kostant-Rosenberg map for graded manifolds. International Mathematics Research Notices, 2005(62):3899-3918.

## 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 C∞(N)) is an isomorphism of Batalin–Vilkovisky algebras. These results generalize to differential graded manifolds.

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 C∞(N)) is an isomorphism of Batalin–Vilkovisky algebras. These results generalize to differential graded manifolds.