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 (resp. , odd) and the surface group is maximal in some (resp. ). This is a converse, for classical groups, to a rigidity result of S. Bradlow, O. García-Prada and P. Gothen.
Cite this article
Inkang Kim, Pierre Pansu, Flexibility of surface groups in classical simple Lie groups. J. Eur. Math. Soc. 17 (2015), no. 9, pp. 2209–2242DOI 10.4171/JEMS/555