Flexibility of surface groups in classical simple Lie groups (Q747608)
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scientific article; zbMATH DE number 6495633
| Language | Label | Description | Also known as |
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| English | Flexibility of surface groups in classical simple Lie groups |
scientific article; zbMATH DE number 6495633 |
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Flexibility of surface groups in classical simple Lie groups (English)
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16 October 2015
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Summary: 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 \textit{S. B. Bradlow} et al. [J. Differ. Geom. 64, No. 1, 111--170 (2003; Zbl 1070.53054); Geom. Dedicata 122, 185--213 (2006; Zbl 1132.14029)].
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algebraic group
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symmetric space
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rigidity
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group cohomology
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moduli space
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