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

• Type: Article in International Scientific Journal
• Date: 2001

Authors

bradlow, sb (Author) Other; garcía-prada, o (Author) Other; gothen, pb (Author) FCUP

Journal

The Journal is awaiting validation by the Administrative Services.

Title: COMPTES RENDUS DE L ACADEMIE DES SCIENCES SERIE I-MATHEMATIQUE

Vol. 333

Pages: 347-352

ISSN: 0764-4442

Indexing

ISI Web of Knowledge - 7 Citations

Scopus - 7 Citations

Other information

Authenticus ID: P-000-TM5

DOI: 10.1016/s0764-4442(01)02069-9

Abstract (EN): 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 nonempty and irreducible. (C) 2001 Academie des sciences/Editions scientifiques et medicales Elsevier SAS.

Language: English

Type (Professor's evaluation): Scientific

No. of pages: 6