On the cohomology of the moduli space of parabolic connections

Abstract

We study the moduli space of logarithmic connections of rank 2 on $${\mathbb {P}}^1 {\setminus } \{ t_1, \dots , t_5 \}$$ with fixed spectral data. The aim of this paper is to compute the cohomology of this space, a computation that will be used to extend the results of the Geometric Langlands Correspondence due to D. Arinkin to the case where these types of connections have five simple poles on $${\mathbb {P}}^1$$ .