Groups, Geometry, and Dynamics


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Volume 11, Issue 1, 2017, pp. 311–352
DOI: 10.4171/GGD/398

Published online: 2017-04-20

Real reflections, commutators, and cross-ratios in complex hyperbolic space

Julien Paupert[1] and Pierre Will[2]

(1) Arizona State University, Tempe, USA
(2) Université de Grenoble I, France

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,$\mathcal{O}_d)$ with $d=1,2,3,7,11$ are generated by real reflections up to index 1, 2, 4 or 8.

Keywords: Complex hyperbolic geometry, reflection groups

Paupert Julien, Will Pierre: Real reflections, commutators, and cross-ratios in complex hyperbolic space. Groups Geom. Dyn. 11 (2017), 311-352. doi: 10.4171/GGD/398