The homology of the little disks operad

Abstract

In this expository paper we give an elementary, hands-on computation of the homology of the little disks operad, showing that the homology of a $d-fold loop space is a Poisson algebra. One aim is to familiarize a greater audience with Euclidean configuration spaces, using tools accessible to second-year graduate students. We also give a brief introduction to the theory of operads. New results include identifying the pairing between homology and cohomology of these spaces as a pairing of graphs and trees, and treating the cooperad structure on cohomology.