Poincare Koszul duality and factorization homology

11 November 2013
Factorization homology is an invariant of an n-manifold M together with an n-disk algebra A. Should M be a circle, this recovers the Hochschild complex of A; should A be a commutative algebra, this recovers the homology of M with coefficients in A. In general, factorization homology retains more information about a manifold than its underlying homotopy type. In this talk we will lift Poincare' duality to factorization homology as it intertwines with Koszul duality for n-disk algebras -- all terms will be explained. We will point out a number of consequences of this duality, which concern manifold invariants as well as algebra invariants. This is a report on joint work with John Francis.