On the Cohomology of Moduli Space of Parabolic Connections

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 such space, and this computation will be used to extend the results of Geometric Langlands Correspondence due to D. Arinkin to the case where this type of connections have five simple poles on ${\mathbb{P}}^1$.