TY - JOUR

T1 - Représentations du groupe fondamental d'une surface dans PU(p,q) et triplets holomorphes

AU - Bradlow, Steven B.

AU - García-Prada, Oscar

AU - Gothen, Peter B.

N1 - Funding Information:
Acknowledgements. We thank the mathematics departments of the University of Illinois at Urbana-Champaign and the Universidad Autónoma de Madrid, the Department of Pure Mathematics of the University of Porto and the Mathematical Institute of the University of Oxford for their hospitality during various stages of this research. The authors are members of VBAC (Vector Bundles on Algebraic Curves), which is partially supported by EAGER (EC FP5 Contract no. HPRN-CT-2000-00099) and by EDGE (EC FP5 Contract no. HPRN-CT-2000-00101). The first author was supported in part by the National Science Foundation under grant n◦ DMS-0072073. The second author was partially supported by the Ministerio de Ciencia y Tecnología (Spain) under grant n◦ BFM2000-0024. The third author was partially supported by the Fundação para a Ciência e a Tecnologia (Portugal) through the Centro de Matemática da Universidade do Porto and through grant no. SFRH/BPD/1606/2000.

PY - 2001/8/15

Y1 - 2001/8/15

N2 - We count the connected components in the moduli space of PU(p,q)-representations of the fundamental group for a closed oriented surface. The components are labelled by pairs of integers which arise as topological invariants of the flat bundles associated to the representations. Our results show that for each allowed value of these invariants, which are bounded by a Milnor-Wood type inequality, there is a unique non-empty connected component. Interpreting the moduli space of representations as a moduli space of Higgs bundles, we take a Morse theoretic approach using a certain smooth proper function on the Higgs moduli space. A key step is the identification of the function's local minima as moduli spaces of holomorphic triples. We prove that these moduli spaces of triples are non-empty and irreducible.

AB - We count the connected components in the moduli space of PU(p,q)-representations of the fundamental group for a closed oriented surface. The components are labelled by pairs of integers which arise as topological invariants of the flat bundles associated to the representations. Our results show that for each allowed value of these invariants, which are bounded by a Milnor-Wood type inequality, there is a unique non-empty connected component. Interpreting the moduli space of representations as a moduli space of Higgs bundles, we take a Morse theoretic approach using a certain smooth proper function on the Higgs moduli space. A key step is the identification of the function's local minima as moduli spaces of holomorphic triples. We prove that these moduli spaces of triples are non-empty and irreducible.

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U2 - 10.1016/S0764-4442(01)02069-9

DO - 10.1016/S0764-4442(01)02069-9

M3 - Article

AN - SCOPUS:18044403621

SN - 0764-4442

VL - 333

SP - 347

EP - 352

JO - Comptes Rendus de l'Academie des Sciences - Series I: Mathematics

JF - Comptes Rendus de l'Academie des Sciences - Series I: Mathematics

IS - 4

ER -