## Covering spaces of 3-manifolds.(English)Zbl 0624.57016

Let M be an arbitrary closed $$P^ 2$$-irreducible 3-manifold. The authors announce, and outline the proofs, of the following two theorems. If $$\pi_ 1(M)$$ contains the fundamental group of a closed surface other than $$S^ 2$$ or $$P^ 2$$, then the universal covering of M is $${\mathbb{R}}^ 3$$. If $$\pi_ 1(M)$$ contains $${\mathbb{Z}} \times {\mathbb{Z}}$$, the every covering of M with fundamental group $${\mathbb{Z}} \times {\mathbb{Z}}$$ can be compactified by adding boundary to it.
Reviewer: J.Vrabec

### MSC:

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

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