- journal article metadata
European Mathematical Society Publishing House
2017-04-23 23:45:01
Groups, Geometry, and Dynamics
Groups Geom. Dyn.
GGD
1661-7207
1661-7215
Group theory and generalizations
10.4171/GGD
http://www.ems-ph.org/doi/10.4171/GGD
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European Mathematical Society Publishing House
Zuerich, Switzerland
© European Mathematical Society
11
2017
1
Real reflections, commutators, and cross-ratios in complex hyperbolic space
Julien
Paupert
Arizona State University, TEMPE, UNITED STATES
Pierre
Will
Université de Grenoble I, SAINT-MARTIN D'HÈRES, FRANCE
Complex hyperbolic geometry, reflection groups
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.
Geometry
Topological groups, Lie groups
311
352
10.4171/GGD/398
http://www.ems-ph.org/doi/10.4171/GGD/398