Communications in Analysis and Geometry

Volume 18 (2010)

Number 1

Connected components of spaces of representations of non-orientable surfaces

Pages: 195 – 217

DOI: http://dx.doi.org/10.4310/CAG.2010.v18.n1.a8

Author

Frederic Palesi (Institut Fourier, St Martin d’Heres, France)

Abstract

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.

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