Peter B. Gothen
Published 2000-12-11, updated 2002-11-28Version 2
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.
Comments: 12 pages, published version. Contains a more careful discussion of the relation between the fixed and non-fixed determinant moduli spaces
Journal: Bull. London Math. Soc. 34 (2002), 729-738
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