## Compactifying coverings of closed 3-manifolds.(English)Zbl 0693.57011

It is shown that a closed, $$P^ 2$$-irreducible 3-manifold M such that $$\pi_ 1(M)$$ contains the fundamental group of a closed surface of negative Euler characteristic has its universal cover $$\tilde M$$ homeomorphic to $${\mathbb{R}}^ 3$$. This can be rephrased by saying that $$\tilde M$$ is almost compact - has a manifold compactification. A second result shows that if M is a closed, $$P^ 2$$-irreducible 3-manifold such that $$\pi_ 1(M)$$ has a subgroup isomorphic to $${\mathbb{Z}}\times {\mathbb{Z}}$$ then the covering of M corresponding to this subgroup is almost compact.
Reviewer: J.Hempel

### MSC:

 57N10 Topology of general $$3$$-manifolds (MSC2010) 57M10 Covering spaces and low-dimensional topology
Full Text: