Poincaré/Koszul duality

Abstract

We prove a duality for factorization homology which generalizes both usual Poincaré duality for manifolds and Koszul duality for ${\mathcal{E}}_n$-algebras. The duality has application to the Hochschild homology of associative algebras and enveloping algebras of Lie algebras. We interpret our result at the level of topological quantum field theory.

70 pages, final version, accepted by Communications in Mathematical Physics