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 $\Sigma^\infty_+ E_M$.