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

  • Julien Paupert

    Arizona State University, Tempe, USA
  • Pierre Will

    Université de Grenoble I, France

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