Parabolic Higgs bundles and Teichmuller spaces for punctured surfaces

In this paper we study the relation between parabolic Higgs vector bundles and irreducible representations of the fundamental group of punctured Riemann surfaces established by Simpson. We generalize a result of Hitchin, identifying those parabolic Higgs bundles that correspond to Fuchsian representations. We also study the Higgs bundles that give representations whose image is contained, after conjugation, in SL(k,R). We compute the real dimension of one of the components of this space of representations, which in the absence of punctures is the generalized Teichmuller space introduced by Hitchin, and which in the case of k = 2 is the usual Teichmuller space of the punctured surface.