Freedman, Michael H.; Gabai, David Covering a nontaming knot by the unlink. (English) Zbl 1158.57024 Algebr. Geom. Topol. 7, 1561-1578 (2007). A 3-manifold is non-tame if it is not homeomorphic to the interior of a compact manifold. A non-taming knot is a smooth simple closed curve \(\gamma\) in a 3-manifold \(M\) such that \(\pi_1(M)\) is finitely generated and \(\pi_1(M-\gamma)\) is infinitely generated.This paper provides an example of a knot in a non-tame manifold \(M\), which is non-taming although it lifts to the unlink in the universal covering \(\mathbb{R}^3\). Reviewer: Luigi Grasselli (Reggio Emilia) Cited in 1 Document MSC: 57N10 Topology of general \(3\)-manifolds (MSC2010) 57M10 Covering spaces and low-dimensional topology 57N45 Flatness and tameness of topological manifolds Keywords:Marden conjecture; nontaming knot; tameness PDFBibTeX XMLCite \textit{M. H. Freedman} and \textit{D. Gabai}, Algebr. Geom. Topol. 7, 1561--1578 (2007; Zbl 1158.57024) Full Text: DOI References: [1] I Agol, Tameness of hyperbolic 3-manifolds [2] D Calegari, D Gabai, Shrinkwrapping and the taming of hyperbolic 3-manifolds, J. Amer. Math. Soc. 19 (2006) 385 · Zbl 1090.57010 [3] D Gabai, Foliations and the topology of \(3\)-manifolds, J. Differential Geom. 18 (1983) 445 · Zbl 0539.57013 [4] A Marden, The geometry of finitely generated kleinian groups, Ann. of Math. \((2)\) 99 (1974) 383 · Zbl 0282.30014 [5] R Myers, End reductions, fundamental groups, and covering spaces of irreducible open 3-manifolds, Geom. Topol. 9 (2005) 971 · Zbl 1092.57002 [6] R Roussarie, Plongements dans les variétés feuilletées et classification de feuilletages sans holonomie, Inst. Hautes Études Sci. Publ. Math. (1974) 101 · Zbl 0356.57017 [7] J Stallings, On fibering certain \(3\)-manifolds (editor M Fort), Prentice-Hall (1962) 95 · Zbl 1246.57049 [8] T W Tucker, Non-compact 3-manifolds and the missing-boundary problem, Topology 13 (1974) 267 · Zbl 0289.57009 [9] F Waldhausen, On irreducible 3-manifolds which are sufficiently large, Ann. of Math. \((2)\) 87 (1968) 56 · Zbl 0157.30603 This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.