Real reflections, commutators, and cross-ratios in complex hyperbolic space
Julien Paupert
Arizona State University, Tempe, USAPierre Will
Université de Grenoble I, France
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Abstract
We provide a concrete criterion to determine whether or not two given elements of PU(2,1) can be written as products of real reflections, with one reflection in common. As an application, we show that the Picard modular groups PU(2,1, with are generated by real reflections up to index 1, 2, 4 or 8.
Cite this article
Julien Paupert, Pierre Will, Real reflections, commutators, and cross-ratios in complex hyperbolic space. Groups Geom. Dyn. 11 (2017), no. 1, pp. 311–352
DOI 10.4171/GGD/398