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Transactions of the American Mathematical Society
Transactions of the American Mathematical Society
ISSN 1088-6850(online) ISSN 0002-9947(print)

 

Parabolic Higgs bundles and Teichmüller spaces for punctured surfaces


Authors: Indranil Biswas, Pablo Arés-Gastesi and Suresh Govindarajan
Journal: Trans. Amer. Math. Soc. 349 (1997), 1551-1560
MSC (1991): Primary 58E15, 58E20, 32G15; Secondary 14E99
MathSciNet review: 1407481
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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($k,\mathbb R$). 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.


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Additional Information

Indranil Biswas
Affiliation: School of Mathematics, Tata Institute of Fundamental Research, Bombay, India
Email: indranil@math.tifr.res.in

Pablo Arés-Gastesi
Email: pablo@math.tifr.res.in

Suresh Govindarajan
Affiliation: Department of Physics, Indian Institute of Technology, Madras, India
Email: suresh@imsc.ernet.in

DOI: http://dx.doi.org/10.1090/S0002-9947-97-01870-9
PII: S 0002-9947(97)01870-9
Keywords: Higgs bundles, parabolic bundles, hermitian metric
Received by editor(s): October 24, 1995
Article copyright: © Copyright 1997 American Mathematical Society