BV structure on the Hochschild cohomology of Sullivan algebras

Let X be a closed, simply connected manifold of dimension m and LX the space of free loops on X. If (∧V, d) is the minimal Sullivan model of X where V is finite dimensional, then there is a Gerstenhaber algebra (∧V⊗∧s−1V#,d0), where V# is the graded dual of V, and its homology is isomorphic to the loop space homology H*(LX). In this paper we define a BV structure on (∧V⊗∧s−1V#,d0) which extends the Gerstenhaber bracket.