## 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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