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- Steven B. Bradlow, Oscar Garćıa–Prada, Peter B. Gothen
- 2002

Using the L 2 norm of the Higgs field as a Morse function, we study the moduli spaces of U(p, q)-Higgs bundles over a Riemann surface. We require that the genus of the surface be at least two, but place no constraints on (p, q). A key step is the identification of the function's local minima as moduli spaces of holomorphic triples. In a companion paper [7]… (More)

- Peter B. Gothen
- 1999

We consider the moduli spaces of representations of the fundamental group of a surface of genus g > 2 in the Lie groups SU(2; 2) and Sp(4; R). It is well known that there is a characteristic number, d , of such a representation, satisfying the inequality jdj 6 2g ? 2. This allows one to write the moduli space as a union of subspaces indexed by d , each of… (More)

Several important cases of vector bundles with extra structure (such as Higgs bundles and triples) may be regarded as examples of twisted representations of a finite quiver in the category of sheaves of modules on a variety/manifold/ringed space. We show that the category of such representations is an abelian category with enough injectives by constructing… (More)

Higgs bundles and non-abelian Hodge theory provide holomorphic methods with which to study the moduli spaces of surface group representations in a reduc-tive Lie group G. In this paper we survey the case in which G is the isometry group of a classical Hermitian symmetric space of non-compact type. Using Morse theory on the moduli spaces of Higgs bundles, we… (More)

- P. B. GOTHEN
- 2000

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… (More)

- O Garc´ia-Prada, P B Gothen, I Mundet, I Riera
- 2009

We develop a complete Hitchin–Kobayashi correspondence for twisted pairs on a compact Riemann surface X. The main novelty lies in a careful study of the the notion of polystability for pairs, required for having a bijective correspondence between solutions to the Hermite–Einstein equations, on one hand, and polystable pairs, on the other. Our results allow… (More)

- Steven B. Bradlow, Oscar Garcia-Prada, Peter B. Gothen, Oscar Garćıa–Prada
- 2002

A holomorphic triple over a compact Riemann surface consists of two holo-morphic vector bundles and a holomorphic map between them. After fixing the topo-logical types of the bundles and a real parameter, there exist moduli spaces of stable holomorphic triples. In this paper we study non-emptiness, irreducibility, smoothness, and birational descriptions of… (More)

- Steven B. Bradlow, Oscar Garćıa–Prada, Peter B. Gothen
- 2002

a Ciência e a Tecnologia (Portugal) through the Centro de Matemática da Universidade do Porto and through grant no. SFRH/BPD/1606/2000. Abstract. Using the L 2 norm of the Higgs field as a Morse function, we study the moduli spaces of U(p, q)-Higgs bundles over a Riemann surface. We require that the genus of the surface be at least two, but place no… (More)

We calculate certain homotopy groups of the moduli spaces for representations of a compact oriented surface in the Lie groups GL(n, C) and U(p, q). Our approach relies on the interpretation of these representations in terms of Higgs bundles and uses Bott–Morse theory on the corresponding moduli spaces.

Nous démontrons qu'uné economie d'´ echange (définie par ses préfé-rences et ses dotations) qui génère une fonction de demande excéden-taire aggrégée (DEA) z est proche de l'´ economie associéè a la DEA z , perturbation arbitraire de z. Abstract We establish that an exchange economy, i.e., preferences and endowments , that generates a given aggregate excess… (More)