We show that the complex of rational simplicial chains on a compact and triangulated Poincaré duality space of dimension is an coalgebra with duality. This is the structure required for an A version of the cyclic Deligne conjecture. One corollary is that the shifted Hochschild cohomology of the cochain algebra with values in has a BV structure. This implies, if is moreover simply connected, that the shifted homology of the free loop space admits a BV structure. An appendix by Dennis Sullivan gives a general local construction of structures.
"Infinity structure of Poincaré duality spaces." Algebr. Geom. Topol. 7 (1) 233 - 260, 2007. https://doi.org/10.2140/agt.2007.7.233