Connected components of representation spaces of non-orientable surfaces

Details Connected components of representation spaces of non-orientable surfaces Connected components of representation spaces of non-orientable surfaces

2009-09-13

arxiv.org/abs/0909.2421v1

Mathematics

Geometric Topology

18 pages, 1 figure

Scientific paper

Let M be a compact closed non-orientable surface. We show that the space of
representations of the fundamental group of M into PSL(2,R) has exactly two
connected components. These two components are the preimages of a certain
Stiefel-Whitney characteristic class, computed in a similar way as the Euler
class in the orientable case.

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