Infinity structure of Poincaré duality spaces

Abstract

We show that the complex [math] of rational simplicial chains on a compact and triangulated Poincaré duality space [math] of dimension [math] is an [math] coalgebra with [math] duality. This is the structure required for an A [math] version of the cyclic Deligne conjecture. One corollary is that the shifted Hochschild cohomology [math] of the cochain algebra [math] with values in [math] has a BV structure. This implies, if [math] is moreover simply connected, that the shifted homology [math] of the free loop space admits a BV structure. An appendix by Dennis Sullivan gives a general local construction of [math] structures.