Parabolic Higgs bundles and Teichmüller spaces for punctured surfaces

Details Parabolic Higgs bundles and Teichmüller spaces for punctured surfaces Parabolic Higgs bundles and Teichmüller spaces for punctured surfaces

1995-10-14

arxiv.org/abs/alg-geom/9510011v1

Trans.Am.Math.Soc. 349 (1997) 1551-1560

Physics

High Energy Physics

High Energy Physics - Theory

AMSLaTeX v 2.09, 13 pages, DVI file available at http://www.imsc.ernet.in/~pablo/

Scientific paper

In this paper we study the relation between parabolic Higgs 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($k,\Bbb R$). We compute the real dimension of one of the components of this space of representations, which in the absence of punctures is the generalized Teichm\"uller space introduced by Hitchin, and which in the case of $k=2$ is the Teichm\"uller space of the Riemann surface.

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