Existence of ruled wrappings in hyperbolic 3-manifolds

Abstract

We present a short elementary proof of an existence theorem of certain CAT(-1)-surfaces in open hyperbolic 3-manifolds. The main construction lemma in Calegari and Gabai's proof of Marden's Tameness Conjecture can be replaced by an applicable version of our theorem.

This is the version published by Geometry & Topology on 12 September 2006

References in corpus (2)

• End reductions, fundamental groups, and covering spaces of irreducible open 3-manifolds
• Drilling cores of hyperbolic 3-manifolds to prove tameness

Cited by in corpus (10)

• Effective bilipschitz bounds on drilling and filling
• Marden's Tameness Conjecture: history and applications
• Geometric limits of knot complements
• Bounds on exceptional Dehn filling II
• Bounded Cohomology of Finitely Generated Kleinian Groups
• Volume and structure of hyperbolic 3-manifolds
• Thick hyperbolic 3-manifolds with bounded rank
• Ranks of mapping tori via the curve complex
• Hyperbolization of infinite-type 3-manifolds
• Hausdorff dimension of non-conical limit sets