Flexibility of surface groups in classical simple Lie groups
type: Item
instance of: scholarly article
title: Flexibility of surface groups in classical simple Lie groups
zbMATH Open document ID: 1404.22026
DOI: 10.4171/JEMS/555
author: Inkang Kim
author: Pierre Pansu
published in: Journal of the European Mathematical Society (JEMS)
publication date: 2015-10-16T00:00:00Z
review text: Summary: We show that a surface group of high genus contained in a classical simple Lie group can be deformed to become Zariski dense, unless the Lie group is \(SU(p,q)\) (resp. \(SO^* (2n)\), \(n\) odd) and the surface group is maximal in some \(S(U(p,p) \times U(q-p)) \subset SU(p,q)\) (resp. \(SO^* (2n-2) \times SO(2) \subset SO^* (2n)\)). This is a converse, for classical groups, to a rigidity result of \textit{S. B. Bradlow} et al. [J. Differ. Geom. 64, No. 1, 111--170 (2003; Zbl 1070.53054); Geom. Dedicata 122, 185--213 (2006; Zbl 1132.14029)].
Mathematics Subject Classification ID: 22E40
Mathematics Subject Classification ID: 22E46
Mathematics Subject Classification ID: 57S25
zbMATH DE Number: 6495633
zbMATH Keywords: algebraic group
zbMATH Keywords: symmetric space
zbMATH Keywords: rigidity
zbMATH Keywords: group cohomology
zbMATH Keywords: moduli space
MaRDI profile type: Publication
Wikidata QID: Q115212440
cites work: Surface group representations and \(U(p,q)\)-Higgs bundles.
cites work: Maximal surface group representations in isometry groups of classical Hermitian symmetric spaces
cites work: Surface group representations with maximal Toledo invariant
cites work: Tight homomorphisms and Hermitian symmetric spaces
description: scientific article; zbMATH DE number 6495633