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A note on the construction of a certain class of Kleinian groups

Author: Ricardo Bianconi
Journal: Proc. Amer. Math. Soc. 123 (1995), 3119-3124
MSC: Primary 30F40; Secondary 20H10
MathSciNet review: 1277097
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Abstract: We prove that if $ \{ {S_1},{S_1}', \ldots ,{S_n},S_n'\} $ is a collection of distinct spheres in $ {\mathbb{R}^m}$ with common exterior, and $ {g_1}, \ldots ,{g_n}$ are Möbius transformations such that for each i, $ {S_i}$ is the isometric sphere of $ {g_i}$ and $ S_i'$ is the isometric sphere of $ g_i^{ - 1}$ and such that $ {g_i}$ maps points of contact of $ {S_i}$, to points of contact of $ S_i'$, then the group G generated by the $ {g_i}$'s is Kleinian.

References [Enhancements On Off] (What's this?)

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Keywords: Kleinian groups, parabolic, infinite cycle transformations, isometric spheres, Poincaré's Polyhedron Theorem
Article copyright: © Copyright 1995 American Mathematical Society

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