Hochschild cohomology of intersection complexes and Batalin-Vilkovisky algebras

Let $X$ be a compact, oriented, second countable pseudomanifold. We show that $H{H}_{\bullet }^{\ast }({\tilde{N}}_{\bullet }^{\ast }(X;\mathbb{Q}))$, the Hochschild cohomology of the blown-up intersection cochain complex of $X$, is well defined and endowed with a Batalin-Vilkovisky algebra structure. Furthermore, we prove that it is a topological invariant. More generally, we define the Hochschild cohomology of a perverse differential graded algebra $A_{\bullet }$ and present a natural Gerstenhaber algebra structure on it. This structure can be extended into a Batalin-Vilkovisky algebra when $A_{\bullet }$ is a derived Poincaré duality algebra.