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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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