Of U ( 2 , 1 ) Representation Spaces

N ov 2 00 2 TOPOLOGY OF U ( 2 , 1 ) REPRESENTATION SPACES

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 [14]. This requires a careful analysis of critical submanifolds which turn out to ...

Topology of U(2; 1) Representation Spaces

We calculate 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). In order to obtain our results we use the identiication of this space with an appropriate mod-uli space of Higgs bundles and Morse theory, following Hitchin's programme 11]. This requires a careful analysis of critical subman-ifolds which ...

Branching Theorems for Compact Symmetric Spaces 405 [

A compact symmetric space, for purposes of this article, is a quotient G=K, where G is a compact connected Lie group and K is the identity component of the subgroup of xed points of an involution. A branching theorem describes how an irreducible representation decomposes upon restriction to a subgroup. The article deals with branching theorems for the passage from G to K 2 K 1 , where G=(K 2 K ...

A Representation for Characteristic Functionals of Stable Random Measures with Values in Sazonov Spaces

Approximation of fixed points for a continuous representation of nonexpansive mappings in Hilbert spaces

This paper introduces an implicit scheme for a   continuous representation of nonexpansive mappings on a closed convex subset of a Hilbert space with respect to a   sequence of invariant means defined on an appropriate space of bounded, continuous real valued functions of the semigroup.   The main result is to    prove the strong convergence of the proposed implicit scheme to the unique solutio...