Covering a nontaming knot by the unlink

Freedman, Michael H; Gabai, David

doi:10.2140/agt.2007.7.1561

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Covering a nontaming knot by the unlink

Michael H Freedman and David Gabai

Algebraic & Geometric Topology 7 (2007) 1561–1578

DOI: 10.2140/agt.2007.7.1561

Abstract

There exists an open $3$ –manifold $M$ and a simple closed curve $γ \subset M$ such that $π_{1} (M ∖ γ)$ is infinitely generated, $π_{1} (M)$ 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 $ℝ^{3}$ , 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

References

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

Volume 7, issue 3 (2007)