On the Connectedness of Moduli Spaces of Flat Connections over Compact   Surfaces
  We study the connectedness of the moduli space of gauge equivalence classes of flat G-connections on a compact orientable surface or a compact nonorientable surface for a class of compact connected Lie groups. This class includes all the compact, connected, simply connected Lie groups, and some non-semisimple classical groups including U(n) and Spin^C(n). 
Nan-Kuo Ho, Chiu-Chu Melissa Liu