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Uniform models for the closure of the Riley slice. (English) Zbl 1205.30037

Bonk, Mario (ed.) et al., In the tradition of Ahlfors-Bers, V. Proceedings of the 4th triennial Ahlfors-Bers colloquium, Newark, NJ, USA, May 8–11, 2008. Providence, RI: American Mathematical Society (AMS) (ISBN 978-0-8218-4732-9/pbk). Contemporary Mathematics 510, 249-306 (2010).
The authors consider the space of marked free Kleinian groups generated by two parabolic elements, an extension of the classical Riley slice, which is termed the extended Riley slice. They construct uniform models for Kleinian groups in the extended Riley slice by two distinct methods. By this construction, the authors show that the boundary of the Riley slice is a Jordan curve and that the extended Riley slice coincides with the closure of the Riley slice. Such a result may provide some foundation for the study of deformation spaces of freely decomposable Kleinian groups.
For the entire collection see [Zbl 1185.30001].

MSC:

30F40 Kleinian groups (aspects of compact Riemann surfaces and uniformization)
32G05 Deformations of complex structures
57M50 General geometric structures on low-dimensional manifolds
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