Commensurators of non-free finitely generated Kleinian groups

Abstract

Suppose G is a non-free finitely generated Kleinian group without parabolics which is not a lattice and let C(G) denote the commensurator in PSL(2,C). We prove that if the limit set of G is not a round circle, then C(G) is discrete. Furthermore, G has finite index in C(G) unless G is a fiber group in which case C(G) is a lattice.

15 pages, 1 figure

References in corpus (2)

• Commensurability classes of 2-bridge knot complements
• Quasi-isometric classification of graph manifold groups

Cited by in corpus (5)

• On Discreteness of Commensurators
• Cannon-Thurston Maps for Kleinian Groups
• Commutators, commensurators, and ${\mathrm{PSL}}_2(\mathbb{Z})$
• Commensurators of thin normal subgroups and abelian quotients
• Class number for pseudo-Anosovs