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Covering a nontaming knot by the unlink. (English) Zbl 1158.57024

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 \(\mathbb{R}^3\).

MSC:

57N10 Topology of general \(3\)-manifolds (MSC2010)
57M10 Covering spaces and low-dimensional topology
57N45 Flatness and tameness of topological manifolds
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References:

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