Configuration spaces lecture 7 Stavrou

Описание: Andreas Stavrou
Cohomology of configuration spaces of surfaces as mapping class group representations

In this talk, we focus on the problem of computing the cohomology of the unordered configuration spaces of a manifold as a representation of the mapping class group of the manifold. We give a theorem that computes this representation in terms of the cohomology of the mapping space from the given manifold to a sphere of high enough dimension. We then outline how applying this theorem gives a complete answer to the problem in the case of compact oriented surfaces with one boundary component. Meanwhile we define the terms involved in describing the representations that appear here and deduce how (non)trivial the action of the Johnson filtration is on them.