Connected Components of the Space of Surface Group Representations II
  In math.SG/0303255, we discussed the connected components of the space of surface group representations for any compact connected semisimple Lie group and any closed compact (orientable or nonorientable) surface. In this sequel, we generalize the results in math.SG/0303255 in two directions: we consider general compact connected Lie groups, and we consider all compact surfaces, including the ones with boundaries. We also interpret our results in terms of moduli spaces of flat connections over compact surfaces. 
Nan-Kuo Ho, Chiu-Chu Melissa Liu