Covering a nontaming knot by the unlink

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 ${ℝ}^3$.