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By using Thurston’s bending construction we obtain a sequence of faithful discrete
representations
of the fundamental group of a closed hyperbolic
–manifold
fibering over the circle into the isometry group
of the hyperbolic space
. The algebraic limit
of
contains a finitely
generated subgroup
whose
–dimensional
quotient
has infinitely generated fundamental group, where
is the discontinuity
domain of
acting on
the sphere at infinity
.
Moreover
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