Hass, Joel; Rubinstein, Hyam; Scott, Peter Compactifying coverings of closed 3-manifolds. (English) Zbl 0693.57011 J. Differ. Geom. 30, No. 3, 817-832 (1989). 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 Cited in 5 Documents MSC: 57N10 Topology of general \(3\)-manifolds (MSC2010) 57M10 Covering spaces and low-dimensional topology Keywords:\(P^ 2\)-irreducible 3-manifold; fundamental group; closed surface; Euler characteristic; almost compact × Cite Format Result Cite Review PDF Full Text: DOI