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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

Compactifying sufficiently regular covering spaces of compact 3-manifolds


Author: Robert Myers
Journal: Proc. Amer. Math. Soc. 128 (2000), 1507-1513
MSC (1991): Primary 57M10; Secondary 57N10, 57M60
Published electronically: February 7, 2000
MathSciNet review: 1637416
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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.


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Additional Information

Robert Myers
Affiliation: Department of Mathematics, Oklahoma State University, Stillwater, Oklahoma 74078
Email: myersr@math.okstate.edu

DOI: http://dx.doi.org/10.1090/S0002-9939-00-05109-1
PII: S 0002-9939(00)05109-1
Keywords: 3-manifold, covering space, compactification, hyperbolic 3-manifold
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
Article copyright: © Copyright 2000 American Mathematical Society