Abstract (EN):
The Betti numbers of moduli spaces of representations of a universal central extension of a surface group in the groups U(2, 1) and S U(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.
Language:
English
Type (Professor's evaluation):
Scientific
No. of pages:
10