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Appears in collection : Complex Hyperbolic Geometry and Related Topics / Autour de la géométrie hyperbolique complexe

Viewed as the boundary at infinity of the complex hyperbolic plane, the 3-sphere is equipped with a contact structure. The interplay between this contact structure and limit sets of subgroups of PU(2,1) has deep consequences on the properties of these subgroups. Some limit sets enjoy the property of slimness, that we introduce. Using this property, one can shed new lights on known results, and better describe deformations of subgroups. I will present this notion through simple examples and pictures, and then describe some results we obtain. This is a joint work with E. Falbel and P. Will.

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