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Involution and commutator length for complex hyperbolic isometries. (English) Zbl 1404.32048

Summary: We study decompositions of complex hyperbolic isometries as products of involutions. We show that \(\operatorname{PU}(2,1)\) has involution length 4 and commutator length 1 and that, for all \(n\geqslant 3\), \(\operatorname{PU}(n,1)\) has involution length at most 8.

MSC:

32Q45 Hyperbolic and Kobayashi hyperbolic manifolds
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