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Actions of discrete groups on spheres and real projective spaces

Authors:	Gabriela?Hinojosa Alberto?Verjovsky

Affiliation:	(1) Universidad Autónoma del Estado de Morelos, Av. Universidad 1001, Col. Chamilpa, Cuernavaca, Morelos, MéXICO, 62209;(2) Instituto de Matemáticas, Universidad Nacional Autónoma de México, Unidad Cuernavaca, Av. Universidad s/n, Col. Lomas de Chamilpa, Cuernavaca, Morelos, MéXICO, 62209

Abstract:	In this paper, we first define discrete, smooth actions on $mathbb{S}^{{2n + 1}}$ , whose limit sets are Cantor sets wildly embedded in $mathbb{S}^{{2n + 1}}$ (Antoine's necklaces). Secondly, we define Schottky groups on real projective spaces of odd dimensions, $mathbb{P}^{{2n + 1}}_{mathbb{R}}$ . We lift these actions to (locally) projective actions on the sphere $mathbb{S}^{{2n + 1}}$ and consider the quotient space of the domain of discontinuity by the group to obtain new examples of manifolds with real projective structures. This work was partially supported by PROMEP (SEP). *This work was partially supported by CONACyT (México), grant U1 55084, PAPIIT (UNAM) grant IN102108.

Keywords:	KeywordHeading" >: wild Cantor sets discrete actions and Kleinian Groups
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