Batalin-Vilkovisky algebra structure on the Hochschild cohomology of E_-algebras

When M is a smooth, oriented, compact and simply connected manifold, Luc Menichi has shown that HH^ (C^ (M; F) ), the Hochschild cohomology of the singular cochain complex of M is a Batalin-Vilkovisky algebra. Using the properties of algebras over the Barratt-Eccles operad, we show that this results holds even when the manifold is not simply connected. Furthermore, we prove a similar result for pseudomanifolds. Namely, we explain why HH^_ (N^_ (X;F) ), the Hochschild cohomology of the blown-up intersection cochain complex of a compact, oriented pseudomanifold X, is endowed with a Batalin-Vilkovisky algebra structure.