#### Volume 10, issue 2 (2006)

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Existence of ruled wrappings in hyperbolic $3$–manifolds

### Teruhiko Soma

Geometry & Topology 10 (2006) 1173–1184
 arXiv: 0903.0166
##### Abstract

We present a short elementary proof of an existence theorem of certain $CAT\left(-1\right)$–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. Finally, we will give a short proof of the conjecture along their ideas.

##### Keywords
hyperbolic $3$–manifolds, ruled wrappings, Marden's tameness conjecture
Primary: 57M50
Secondary: 30F40