BV structure on the Hochschild cohomology of Sullivan algebras

Abstract

Abstract 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 − 1 V # , d 0 ) , where V # is the graded dual of V , and its homology is isomorphic to the loop space homology H * ( L X ) . In this paper we define a BV structure on ( ∧ V ⊗ ∧ s − 1 V # , d 0 ) which extends the Gerstenhaber bracket.