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. 2209–2242