Geodesic
Real reflections, commutators, and cross-ratios in complex hyperbolic space
Julien Paupert1 ; Pierre Will2
1Arizona State University, Tempe, USA
2Université de Grenoble I, France
Groups, geometry, and dynamics, Tome 11 (2017) no. 1, pp. 311-352

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DOI

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,Od​) with d=1,2,3,7,11 are generated by real reflections up to index 1, 2, 4 or 8.
DOI : 10.4171/ggd/398
Classification : 51-XX, 22-XX
Mots-clés : Complex hyperbolic geometry, reflection groups

Julien Paupert  1   ; Pierre Will  2

1 Arizona State University, Tempe, USA
2 Université de Grenoble I, France 
Julien Paupert; Pierre Will. Real reflections, commutators, and cross-ratios in complex hyperbolic space. Groups, geometry, and dynamics, Tome 11 (2017) no. 1, pp. 311-352. doi: 10.4171/ggd/398
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     title = {Real reflections, commutators, and cross-ratios in complex hyperbolic space},
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     year = {2017},
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     number = {1},
     doi = {10.4171/ggd/398},
     url = {http://geodesic.mathdoc.fr/articles/10.4171/ggd/398/}
}
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