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Parabolic Higgs bundles and Teichmüller spaces for punctured surfaces

Published in American Mathematical Society
1997
Volume: 349
   
Issue: 4
Pages: 1551 - 1560
Abstract
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(fc,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 Teichmüller space introduced by Hitchin, and which in the case of k = 2 is the usual Teichmüller space of the punctured surface. ©1997 American Mathematical Society.
About the journal
JournalTransactions of the American Mathematical Society
PublisherAmerican Mathematical Society
ISSN00029947
Open AccessNo