Compactifying sufficiently regular covering spaces of compact 3-manifolds
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Abstract:
In this paper it is proven that if the group of covering translations of the covering space of a compact, connected, $\mathbf {P}^2$-irreducible 3-manifold corresponding to a non-trivial, finitely-generated subgroup of its fundamental group is infinite, then either the covering space is almost compact or the subgroup is infinite cyclic and has normalizer a non-finitely-generated subgroup of the rational numbers. In the first case additional information is obtained which is then used to relate Thurston’s hyperbolization and virtual bundle conjectures to some algebraic conjectures about certain 3-manifold groups.References
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Additional Information
- Robert Myers
- Affiliation: Department of Mathematics, Oklahoma State University, Stillwater, Oklahoma 74078
- Email: myersr@math.okstate.edu
- Received by editor(s): October 7, 1997
- Received by editor(s) in revised form: June 1, 1998
- Published electronically: February 7, 2000
- Additional Notes: Research at MSRI is supported in part by NSF grant DMS-9022140.
- Communicated by: Ronald A. Fintushel
- © Copyright 2000 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 128 (2000), 1507-1513
- MSC (1991): Primary 57M10; Secondary 57N10, 57M60
- DOI: https://doi.org/10.1090/S0002-9939-00-05109-1
- MathSciNet review: 1637416