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

Translated title of the contribution: Representations of the fundamental group of a surface in PU(p,q) and holomorphic triples

Steven B. Bradlow, Oscar García-Prada, Peter B. Gothen

Research output: Contribution to journalArticlepeer-review

Abstract

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.

Translated title of the contributionRepresentations of the fundamental group of a surface in PU(p,q) and holomorphic triples
Original languageFrench
Pages (from-to)347-352
Number of pages6
JournalComptes Rendus de l'Academie des Sciences - Series I: Mathematics
Volume333
Issue number4
DOIs
StatePublished - Aug 15 2001

ASJC Scopus subject areas

  • Mathematics(all)

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