Communications in Analysis and Geometry
Volume 18 (2010)
Connected components of spaces of representations of non-orientable surfaces
Pages: 195 – 217
Let $M$ be a compact closed non-orientable surface. We showthat the space of representations of the fundamental groupof $M$ into $\psl$ has exactly two connected components.These two components are the preimages of a certainStiefel–Whitney characteristic class, computed in a similarway as the Euler class in the orientable case.