JournalsjemsVol. 17, No. 9pp. 2209–2242

Flexibility of surface groups in classical simple Lie groups

  • Inkang Kim

    KIAS, Seoul, South Korea
  • Pierre Pansu

    Université Paris-Sud 11, Orsay, France
Flexibility of surface groups in classical simple Lie groups cover
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Abstract

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)SU(p,q) (resp. SO(2n)SO^* (2n), nn odd) and the surface group is maximal in some S(U(p,p)×U(qp))SU(p,q)S(U(p,p) \times U(q-p)) \subset SU(p,q) (resp. SO(2n2)×SO(2)SO(2n)SO^* (2n-2) \times SO(2) \subset SO^* (2n)). 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

DOI 10.4171/JEMS/555