Geodesic
On the geometry of a Picard modular group
Martin Deraux1
1Université Grenoble Alpes, Gières, France
Groups, geometry, and dynamics, Tome 17 (2023) no. 4, pp. 1393-1416

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DOI

We study geometric properties of the action on the complex hyperbolic plane HC2​ of the Picard modular group Γ=PU(2,1,O7​), where O7​ denotes the ring of algebraic integers in Q(i7​). We list conjugacy classes of maximal finite subgroups in Γ and give an explicit description of the Fuchsian subgroups that occur as stabilizers of mirrors of complex reflections in Γ. As an application, we describe an explicit torsion-free subgroup of index 336 in Γ.
DOI : 10.4171/ggd/734
Classification : 22-XX, 32-XX
Mots-clés : Arithmetic groups, locally symmetric spaces, complex hyperbolic geometry

Martin Deraux  1

1 Université Grenoble Alpes, Gières, France 
Martin Deraux. On the geometry of a Picard modular group. Groups, geometry, and dynamics, Tome 17 (2023) no. 4, pp. 1393-1416. doi: 10.4171/ggd/734
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     year = {2023},
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     number = {4},
     doi = {10.4171/ggd/734},
     url = {http://geodesic.mathdoc.fr/articles/10.4171/ggd/734/}
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