# Configurations of Lagrangians, fundamental domains and discrete subgroups of PU(2,1).

Abstract : The object of this thesis is to investigate discrete subgroups of
$PU(2,1)$, the group of holomorphic isometries of complex hyperbolic space of (complex) dimension 2. We are mostly concerned with those groups generated by elliptic motions, i.e. motions fixing a point of this space.

The two guiding principles of this work are on one hand the use of
Lagrangian subspaces (or real planes) and their associated reflections (antiholomorphic involutions), and on the other hand the study and understanding of the examples of lattices in $PU(2,1)$ which Mostow constructed in 1980.
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Cited literature [104 references]

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Submitted on : Tuesday, January 31, 2006 - 1:22:21 PM
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• HAL Id : tel-00011502, version 1

### Citation

Julien Paupert. Configurations of Lagrangians, fundamental domains and discrete subgroups of PU(2,1).. Mathematics [math]. Université Pierre et Marie Curie - Paris VI, 2005. English. ⟨tel-00011502⟩

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