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TOPOLOGY OF $U(2, 1)$ REPRESENTATION SPACES

Published online by Cambridge University Press:  24 March 2003

PETER B. GOTHEN
PETER B. GOTHEN
Affiliation:
Departamento de Matemática Pura, Faculdade de Ciências, Rua do Campo Alegre 687, 4169–007 Porto, Portugalpbgothen@fc.up.pt
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Abstract

The Betti numbers of moduli spaces of representations of a universal central extension of a surface group in the groups $U(2, 1)$ and $SU(2, 1)$ are calculated. The results are obtained using the identification of these moduli spaces with moduli spaces of Higgs bundles, and Morse theory, following Hitchin's programme. This requires a careful analysis of critical submanifolds, which turn out to have a description using either symmetric products of the surface or moduli spaces of Bradlow pairs.

Type
NOTES AND PAPERS
Information
Bulletin of the London Mathematical Society , Volume 34 , Issue 6 , November 2002 , pp. 729 - 738
Copyright
© The London Mathematical Society 2002

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Footnotes

Partially supported by the Fundação para a Ciência e a Tecnologia (Portugal) through the Centro de Matemática da Universidade do Porto, and by the European Commission through the Research Training Networks EAGER and EDGE (Contracts Nos HPRN-CT-2000-00099 and HPRN-CT-2000-00101).