Flexibility of surface groups in classical simple Lie groups (Q747608)

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)].