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Let $X$ be a compact, oriented, second countable pseudomanifold. We show that$HH^\ast_\bullet(\widetilde N^\ast_\bullet(X;\mathbb{Q}))$, the Hochschildcohomology of the blown-up intersection cochain complex of $X$, is well definedand endowed with a Batalin-Vilkovisky algebra structure. Furthermore, we provethat it is a topological invariant. More generally, we define the Hochschildcohomology of a perverse differential graded algebra $A_\bullet$ and present anatural Gerstenhaber algebra structure on it. This structure can be extendedinto a Batalin-Vilkovisky algebra when $A_\bullet$ is a derived Poincar\'eduality algebra.

Hochschild cohomology of intersection complexes and Batalin-Vilkovisky algebras