Components of spaces of representations and stable triples

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

Authors

Gothen, PB (Author) FCUP

Journal

Title: Topology

Vol. 40

Pages: 823-850

ISSN: 0040-9383

Publisher: Pergamon Press - Elsevier

Indexing

ISI Web of Knowledge - 47 Citations

Scopus - 48 Citations

Scientific classification

FOS: Natural sciences > Mathematics

Other information

Authenticus ID: P-000-V5C

DOI: 10.1016/s0040-9383(99)00086-5

Abstract (EN): We consider the moduli spaces of representations of the fundamental group of a surface of genus g greater than or equal to 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 \d\ less than or equal to 2g - 2. This allows one to write the moduli space as a union of subspaces indexed by d, each of which is a union of connected components. The main result of this paper is that the subspaces corresponding to d = +/- (2g - 2) are connected in the case of representations in SU(2,2), while they break up into 3 . 2(2g) + 2g - 4 connected components in the case of representations in Sp(4, R). We obtain our results using the interpretation of the moduli space of representations as a moduli space of Higgs bundles, and an important step is an identification of certain subspaces as moduli spaces of stable triples, as studied by Bradlow and Garcia-Prada.

Language: English

Type (Professor's evaluation): Scientific

No. of pages: 28