Compactifying sufficiently regular covering spaces of compact 3-manifolds

Myers, Robert

doi:10.1090/S0002-9939-00-05109-1

Compactifying sufficiently regular covering spaces of compact 3-manifolds
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Proc. Amer. Math. Soc. 128 (2000), 1507-1513 Request permission

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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