Cohomology Algebra of the configuration Spaces of Riemann Surfaces

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 .