Geometry & Topology Monographs 1 (1998) 479–492

DOI: 10.2140/gtm.1998.1.479

arXiv: math.GT/9811181

Abstract

By using Thurston's bending construction we obtain a sequence of faithful discrete representations ρ_n of the fundamental group of a closed hyperbolic 3–manifold fibering over the circle into the isometry group Iso H⁴ of the hyperbolic space H⁴ . The algebraic limit of ρ_n contains a finitely generated subgroup F whose 3–dimensional quotient Ω(F)/F has infinitely generated fundamental group, where Ω(F) is the discontinuity domain of F acting on the sphere at infinity S³_∞=∂H⁴. Moreover F is isomorphic to the fundamental group of a closed surface and contains infinitely many conjugacy classes of maximal parabolic subgroups.

Keywords

discrete (Kleinian) subgroups, deformation spaces, hyperbolic 4–manifolds, conformally flat 3–manifolds, surface bundles over the circle

Mathematical Subject Classification

Primary: 20H10, 30F40, 57M10

Secondary: 30F10, 30F35, 57M05, 57S30

References

Publication

Received: 20 November 1997
Revised: 7 November 1998
Published: 17 November 1998

Authors