Topology of U(2,1) representation spaces

Details Topology of U(2,1) representation spaces Topology of U(2,1) representation spaces

2000-12-11

arxiv.org/abs/math/0012074v2

Bull. London Math. Soc. 34 (2002), 729-738

Mathematics

Algebraic Geometry

12 pages, published version. Contains a more careful discussion of the relation between the fixed and non-fixed determinant mo

Scientific paper

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.

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