Surface group representations and U(p, q)-Higgs bundles

• Type: Article in International Scientific Journal
• Date: 2003

Authors

Bradlow, SB (Author) Other; Garcia Prada, O (Author) Other; Gothen, PB (Author) FCUP

Journal

Title: Journal of Differential Geometry

Vol. 64

Pages: 111-170

ISSN: 0022-040X

Publisher: International Press of Boston, Inc.

Indexing

ISI Web of Knowledge - 79 Citations

Scopus - 80 Citations

Scientific classification

FOS: Natural sciences > Mathematics

Other information

Authenticus ID: P-000-GW7

DOI: 10.4310/jdg/1090426889

Abstract (EN): 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] we prove that these moduli spaces of triples are nonempty and irreducible. Because of the relation between flat bundles and fundamental group representations, we can interpret our conclusions as results about the number of connected components in the moduli space of semisimple PU(p, q)-representations. The topological invariants of the flat bundles axe used to label subspaces. These invariants are bounded by a Milnor-Wood type inequality. For each allowed value of the invariants satisfying a certain co-primality condition, we prove that the corresponding subspace is nonempty and connected. If the coprimality condition does not hold, our results apply to the closure of the moduli space of irreducible representations.

Language: English

Type (Professor's evaluation): Scientific

No. of pages: 60