Abstract

Using a density theorem and a drilling theorem of Bromberg we prove a uniqueness result for singly degenerate hyperbolic 3-manifolds without cusps. By results of Minsky on the curve complex and end-invariants we then improve upon this theorem to prove the ending lamination conjecture for singly degenerate hyperbolic 3-manifolds with slender end-invariants. Although this result is known by work of Brock, Canary and Minsky, our proof uses a different approach, in particular avoiding the construction of a model manifold.

Keywords

hyperbolic 3-manifolds, Kleinian groups, ending lamination conjecture

Mathematical Subject Classification

Primary: 57M50

Secondary: 30F40, 57N10

Authors