BATALIN-VILKOVISKY COALGEBRA OF STRING TOPOLOGY

We prove that the reduced Hochschild homology of a commutative DG Frobenius algebra has the natural structure of a Batalin-Vilkovisky coalgebra, and the reduced cyclic homology has the natural structure of a gravity coalgebra. As an application, this gives an algebraic model for a Batalin-Vilkovisky coalgebra structure on the reduced homology of the free loop space of a simply connected closed oriented manifold, and a gravity coalgebra structure on the reduced equivariant homology.