## Algebraic & Geometric Topology

### Covering a nontaming knot by the unlink

#### Abstract

There exists an open $3$–manifold $M$ and a simple closed curve $γ⊂M$ such that $π1(M∖γ)$ is infinitely generated, $π1(M)$ is finitely generated and the preimage of $γ$ in the universal covering of $M$ is equivalent to the standard locally finite set of vertical lines in $ℝ3$, that is, the trivial link of infinitely many components in $ℝ3$.

#### Article information

Source
Algebr. Geom. Topol., Volume 7, Number 3 (2007), 1561-1578.

Dates
Accepted: 27 December 2005
First available in Project Euclid: 20 December 2017

https://projecteuclid.org/euclid.agt/1513796754

Digital Object Identifier
doi:10.2140/agt.2007.7.1561

Mathematical Reviews number (MathSciNet)
MR2366171

Zentralblatt MATH identifier
1158.57024

#### Citation

Freedman, Michael H; Gabai, David. Covering a nontaming knot by the unlink. Algebr. Geom. Topol. 7 (2007), no. 3, 1561--1578. doi:10.2140/agt.2007.7.1561. https://projecteuclid.org/euclid.agt/1513796754

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