Abstract:
In this thesis we study the Kriˇz model E(M, n), for the configuration spaces at
large, for M -an arbitrary smooth complex projective variety, and in particular, for the
family of Riemann surfaces M g with genus g ≥ 1. There is an induced action of the
symmetric group S n on the differential graded algebra E(M, n), some representation
theory of this DGA is studied. The cohomology groups of 2,3 and 4-point ordered
and unordered configuration spaces of Riemann surfaces are computed with tools
borrowed from the representation theory of S n .
