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Published in:
2017 | OriginalPaper | Chapter
Extending the Action of Schottky Groups on the Complex Anti-de Sitter Space to the Projective Space
Authors : Vanessa Alderete, Carlos Cabrera, Angel Cano, Mayra Méndez
Published in: Singularities in Geometry, Topology, Foliations and Dynamics
Publisher: Springer International Publishing
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In this article we show that if a complex Schottky group, acting on the complex anti-de Sitter space, acts on the corresponding projective space as a Schottky group, then the space has signature (k, k): As a consequence, we are able to show the existence of complex Schottky groups, acting on $$ {\mathbb{P}}_\mathbb{C}^n $$, such that the complement of whose Kulkarni's limit set is not the largest open set on which the group acts properly and discontinuously. This is the starting point towards the understanding of the notion of the role of limit sets in the higher-dimensional setting.