Koszul self-duality of manifolds

Abstract

We show that Koszul duality for operads in $(\mathrm{Top},\times )$ can be expressed via generalized Thom complexes. As an application, we prove the Koszul self-duality of the right module $E_M$ associated to a framed manifold $M$. We discuss implications for factorization homology, embedding calculus, and confirm an old conjecture of Ching on the relation of Goodwillie calculus to manifold calculus.