Flexibility of surface groups in classical groups

Details Flexibility of surface groups in classical groups Flexibility of surface groups in classical groups

2011-01-06

arxiv.org/abs/1101.1159v1

Mathematics

Differential Geometry

35 pages

Scientific paper

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.

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