One point compactifications of configuration spaces and the self duality of the little disks operad

Abstract

Using configuration space level Pontryagin--Thom constructions, we construct a simple Koszul self duality map for the little disks operad ${\Sigma }_{+}^{\infty }{E}_n$. For a framed $n$-manifold $M$, we show that a compatible self duality map exists for ${\Sigma }_{+}^{\infty }{E}_M$.

Final version; to appear in Algebraic & Geometric Topology