Remote Access Proceedings of the American Mathematical Society
Green Open Access

Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)

 
 

 

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
DOI: https://doi.org/10.1090/S0002-9939-1995-1277097-0
MathSciNet review: 1277097
Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

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?)

  • [1] M. Bestvina and D. Cooper, A wild Cantor set as the limit set of a conformal group action on $ {S^3}$, Proc. Amer. Math. Soc. 99 (1987), 623-626. MR 877028 (88b:57015)
  • [2] R. Bianconi, N. Gusevskii, and H. Klimenko, Schottky-type groups and Kleinian groups acting on $ {\mathbb{R}^3}$, preprint, 1994.
  • [3] B. Maskit, Kleinian groups, Springer-Verlag, Berlin, 1988. MR 959135 (90a:30132)
  • [4] -, On Klein's combination theorem, Trans. Amer. Math. Soc. 120 (1965), 499-509. MR 0192047 (33:274)

Similar Articles

Retrieve articles in Proceedings of the American Mathematical Society with MSC: 30F40, 20H10

Retrieve articles in all journals with MSC: 30F40, 20H10


Additional Information

DOI: https://doi.org/10.1090/S0002-9939-1995-1277097-0
Keywords: Kleinian groups, parabolic, infinite cycle transformations, isometric spheres, Poincaré's Polyhedron Theorem
Article copyright: © Copyright 1995 American Mathematical Society

American Mathematical Society