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  • LIMIT SETS AND COMMENSURABILITY OF KLEINIAN GROUPS

  • Part of
  • WEN-YUAN YANG, YUE-PING JIANG
  • Journal:
    Bulletin of the Australian Mathematical Society / Volume 82 / Issue 1 / August 2010
    Published online by Cambridge University Press:
    02 June 2010, pp. 1-9
    Print publication:
    August 2010
    • Article
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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.