Abstract:
The ordered configuration space of n points in a topological space X is the space of all possible configurations of n labelled points in that space X. There is a natural action of the symmetric group, Sn, on the ordered configuration space and the quotient under this action is the unordered configuration space.
For a smooth complex projective variety X, I. Kriz constructed a rational model (a differential bigraded algebra) for the ordered configuration space. The Sn-action on the configuration space induces an Sn-action on the Kriz model.
I will discuss this Sn-action and as an application describe the cohomology algebra of 3-points conguration spaces of complex projective spaces.