Poincar\'e/Koszul duality

TL;DR

This paper establishes a duality in factorization homology that unifies Poincaré duality and Koszul duality, with implications for Hochschild homology and topological quantum field theories.

Contribution

It introduces a generalized duality for factorization homology that extends classical Poincaré and Koszul dualities, connecting algebraic and topological structures.

Findings

Proves a duality unifying Poincaré and Koszul dualities.

Applies the duality to Hochschild homology of associative and Lie algebras.

Interprets the duality within topological quantum field theory.

Abstract

We prove a duality for factorization homology which generalizes both usual Poincar\'e 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.