Flexibility of surface groups in classical simple Lie groups

Inkang Kim (1) , Pierre Pansu (2, 3)

1 KIAS - School of Mathematics
2 DMA - Département de Mathématiques et Applications - ENS Paris
3 LM-Orsay - Laboratoire de Mathématiques d'Orsay

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 S. Bradlow, O. Garc\'{\i}a-Prada and P. Gothen.

Mots clés: Algebraic group; symmetric space; rigidity; group cohomology; moduli space; tube type

Domaines: Géométrie différentielle [math.DG]

Inkang Kim, Pierre Pansu. Flexibility of surface groups in classical simple Lie groups. 2011. ⟨hal-00552307⟩