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LIMIT SETS AND COMMENSURABILITY OF KLEINIAN GROUPS

Part of: Riemann surfaces

Published online by Cambridge University Press:  02 June 2010

WEN-YUAN YANG  and
YUE-PING JIANG
WEN-YUAN YANG*
Affiliation:
College of Mathematics and Econometrics, Hunan University, Changsha, Hunan 410082, PR China U.F.R. de Mathématiques, Université de Lille 1, 59655 Villeneuve D’Ascq Cedex, France (email: [email protected])
YUE-PING JIANG
Affiliation:
College of Mathematics and Econometrics, Hunan University, Changsha, Hunan 410082, PR China (email: [email protected])
*
✉For correspondence; e-mail: [email protected]
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Abstract

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In this paper, we obtain several results on the commensurability of two Kleinian groups and their limit sets. We prove that two finitely generated subgroups G1 and G2 of an infinite co-volume Kleinian group G⊂Isom(H3) having Λ(G1)=Λ(G2) are commensurable. In particular, we prove that any finitely generated subgroup H of a Kleinian group G⊂Isom(H3) with Λ(H)=Λ(G) is of finite index if and only if H is not a virtually fibered subgroup.

Keywords

commensurabilitygeometrically finitelimit sethyperbolic element

MSC classification

Secondary: 30F40: Kleinian groups
Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 82 , Issue 1 , August 2010 , pp. 1 - 9
Copyright
Copyright © Australian Mathematical Publishing Association Inc. 2010

Footnotes

The first author is supported by the China-funded Postgraduates Studying Aboard Program for Building Top University. The second author is supported by National Natural Science Foundation of China (No. 10671059) and Doctorate Foundation of the Ministry of Education of China (No. 20060532023).

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