The ending lamination conjecture for hyperbolic three-manifolds with slender end-invariants

Richard Allen Evans

Vol. 225 (2006), No. 2, 231–241

DOI: 10.2140/pjm.2006.225.231

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 2000

Primary: 57M50

Secondary: 30F40, 57N10

Milestones

Received: 21 February 2006

Accepted: 26 February 2006

Published: 1 June 2006