Infinity structure of Poincaré duality spaces

Abstract

We show that the complex C X of rational simplicial chains on a compact and triangulated Poincare duality space X of dimension d is an A1 coalgebra with1 duality. This is the structure required for an A1 version of the cyclic Deligne conjecture. One corollary is that the shifted Hochschild cohomology HH C d .C X;C X/ of the cochain algebra C X with values in C X has a BV structure. This implies, if X is moreover simply connected, that the shifted homology HC dLX of the free loop space admits a BV structure. An appendix by Dennis Sullivan gives a general local construction of1 structures.