#### Volume 7, issue 3 (2007)

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Covering a nontaming knot by the unlink

### Michael H Freedman and David Gabai

Algebraic & Geometric Topology 7 (2007) 1561–1578
##### Abstract

There exists an open $3$–manifold $M$ and a simple closed curve $\gamma \subset M$ such that ${\pi }_{1}\left(M\setminus \gamma \right)$ is infinitely generated, ${\pi }_{1}\left(M\right)$ is finitely generated and the preimage of $\gamma$ in the universal covering of $M$ is equivalent to the standard locally finite set of vertical lines in ${ℝ}^{3}$, that is, the trivial link of infinitely many components in ${ℝ}^{3}$.

##### Keywords
Marden conjecture, nontaming knot, tameness
##### Mathematical Subject Classification 2000
Primary: 57N10
Secondary: 57M10, 57N45
##### Publication
Received: 28 May 2005
Accepted: 27 December 2005
Published: 17 December 2007
##### Authors
 Michael H Freedman Microsoft Corporation David Gabai Department of Mathematics Princeton University Princeton, NJ 08544