REPRESENTATIONS OF SURFACE GROUPS IN THE PROJECTIVE GENERAL LINEAR GROUP

• Type: Article in International Scientific Journal
• Date: 2011

Authors

Oliveira, AG (Author) FCUP

Journal

Title: International Journal of Mathematics

Vol. 22

Pages: 223-279

ISSN: 0129-167X

Publisher: World Scientific

Indexing

ISI Web of Knowledge - 9 Citations

Scopus - 10 Citations

Scientific classification

FOS: Natural sciences > Mathematics

Other information

Authenticus ID: P-002-V8T

DOI: 10.1142/s0129167x11006787

Abstract (EN): Given a closed, oriented surface X of genus g >= 2, and a semisimple Lie group G, let R-G be the moduli space of reductive representations of pi(1) X in G. We determine the number of connected components of R-PGL(n,R- R), for n >= 4 even. In order to have a first division of connected components, we first classify real projective bundles over such a surface. Then we achieve our goal, using holomorphic methods through the theory of Higgs bundles over compact Riemann surfaces. We also show that the complement of the Hitchin component in R-SL(3,R-R) is homotopically equivalent to R-SO(3).

Language: English

Type (Professor's evaluation): Scientific

No. of pages: 57