Abstract
If a finitely presented groupG is negatively curved, automatic or asynchronously automatic thenG has an asynchronously bounded “almost prefix closed” combing. Results in [Br1] and [E] imply that the fundamental group of any closed 3-manifold satisfying Thurston's geometrization conjecture has an asynchronously bounded, almost prefix closed combing.
MAIN THEOREM. IfM is a compactP 2-irreducible 3-manifold,π 1 (M) has an asynchronously bounded, almost prefix closed combing, andH, a subgroup ofπ 1 (M), is quasiconvex with respect to this combing, then the cover ofM corresponding toH is a missing boundary manifold.
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