Realising end invariants by limits of minimally parabolic, geometrically finite groups

@article{Ohshika2005RealisingEI,
  title={Realising end invariants by limits of minimally parabolic, geometrically finite groups},
  author={Ken'ichi Ohshika},
  journal={Geometry \& Topology},
  year={2005},
  volume={15},
  pages={827-890}
}
We shall show that for a given homeomorphism type and a set of end invariants (including the parabolic locus) with necessary topological conditions which a topologically tame Kleinian group with that homeomorphism type must satisfy, there is an algebraic limit of minimally parabolic, geometrically finite Kleinian groups which has exactly that homeomorphism type and end invariants. This shows that the Bers-Sullivan-Thurston density conjecture follows from Marden's conjecture proved by Agol… 
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References

SHOWING 1-10 OF 103 REFERENCES
Geometrically finite kleinian groups and parabolic elements
Let r be a torsion-free geometrically finite Kleinian group. In this paper, we investigate which systems of loxodromic conjugacy classes of P can be simultaneously made parabolic in a group on the
THE CLASSIFICATION OF KLEINIAN SURFACE GROUPS, II: THE ENDING LAMINATION CONJECTURE
Thurston’s Ending Lamination Conjecture states that a hyperbolic 3manifold N with nitely generated fundamental group is uniquely determined by its topological type and its end invariants. In this
The classification of punctured-torus groups.
Thurston’s ending lamination conjecture proposes that a flnitely generated Kleinian group is uniquely determined (up to isometry) by the topology of its quotient and a list of invariants that
Convergence of freely decomposable Kleinian groups
We consider a compact orientable hyperbolic 3-manifold with a compressible boundary. Suppose that we are given a sequence of geometrically finite hyperbolic metrics whose conformal boundary
Kleinian groups and the complex of curves
We examine the internal geometry of a Kleinian surface group and its relations to the asymptotic geometry of its ends, using the combinatorial structure of the complex of curves on the surface. Our
Uniform perfectness of the limit sets of Kleinian groups
In this note, we show, in a quantitative fashion, that the limit set of a non-elementary Kleinian group is uniformly perfect if the quotient orbifold is of Lehner type, i.e., if the space of
Surface groups and 3-manifolds which fiber over the circle
Geometrization theorem, fibered case: Every three-manifold that fibers over the circle admits a geometric decomposition. Double limit theorem: for any sequence of quasi-Fuchsian groups whose
The classification of Kleinian surface groups I : Models and bounds : preprint
We give the first part of a proof of Thurston’s Ending Lamination conjecture. In this part we show how to construct from the end invariants of a Kleinian surface group a “Lipschitz model” for the
Rigidity and topological conjugates of topologically tame Kleinian groups
Minsky proved that two Kleinian groups G1 and G2 are quasiconformally conjugate if they are freely indecomposable, the injectivity radii at all points of H/G1, H/G2 are bounded below by a positive
...
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