LIMIT SETS AND COMMENSURABILITY OF KLEINIAN GROUPS

作者：Yang, Wen Yuan^*; Jiang, Yue Ping

来源：Bulletin of the Australian Mathematical Society, 2010, 82(1): 1-9.

DOI：10.1017/S0004972710000146

• commensurability
• geometrically finite
• limit set
• hyperbolic element

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 G(1) and G(2) of an infinite co-volume Kleinian group G subset of Isom(H(3)) having Lambda(G(1)) = Lambda(G(2)) are commensurable. In particular, we prove that any finitely generated subgroup H of a Kleinian group G subset of Isom(H(3)) with Lambda(H) = Lambda(G) is of finite index if and only if H is not a virtually fibered subgroup.

• 出版日期2010-8
• 单位湖南大学