Poisson structure on character varieties. II

Let G be a complex reductive group and D a finite subset of a compact Riemann surface X. It was shown in [BJ] that the moduli space of G-characters of the complement of D in X has a natural Poisson structure. We show that the moduli space of logarithmic G-connections on X singular over D has a Poisson structure. It is proved that the monodromy map from the moduli space of logarithmic G-connections to the moduli space of G-characters is Poisson structure preserving.