Commentarii Mathematici Helvetici

, Volume 71, Issue 1, pp 362–372

Compactifying coverings of 3-manifolds

  • Michael L. Mihalik
Article

DOI: 10.1007/BF02566425

Cite this article as:
Mihalik, M.L. Commentarii Mathematici Helvetici (1996) 71: 362. doi:10.1007/BF02566425
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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 compactP2-irreducible 3-manifold,π1 (M) has an asynchronously bounded, almost prefix closed combing, andH, a subgroup ofπ1 (M), is quasiconvex with respect to this combing, then the cover ofM corresponding toH is a missing boundary manifold.

1991 Mathematics Subject Classification

57N1057M1020F32

Copyright information

© Birkhäuser Verlag 1996

Authors and Affiliations

  • Michael L. Mihalik
    • 1
  1. 1.Department of MathematicsVanderbilt UniversityNashvilleU.S.A.