Compactifying sufficiently regular covering spaces of compact 3-manifolds

Details Compactifying sufficiently regular covering spaces of compact 3-manifolds Compactifying sufficiently regular covering spaces of compact 3-manifolds

1997-06-18

arxiv.org/abs/math/9706218v1

Mathematics

Geometric Topology

Scientific paper

In this paper it is proven that if the group of covering translations of the covering space of a compact, connected, $P^2$-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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