Geodesic
Covering a nontaming knot by the unlink
Freedman, Michael H1 ; Gabai, David2
1Microsoft Corporation
2Department of Mathematics, Princeton University, Princeton, NJ 08544
Algebraic and Geometric Topology, Tome 7 (2007) no. 3, pp. 1561-1578
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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.

DOI : 10.2140/agt.2007.7.1561
Keywords: Marden conjecture, nontaming knot, tameness

Freedman, Michael H  1   ; Gabai, David  2

1 Microsoft Corporation
2 Department of Mathematics, Princeton University, Princeton, NJ 08544 
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Freedman, Michael H; Gabai, David. Covering a nontaming knot by the unlink. Algebraic and Geometric Topology, Tome 7 (2007) no. 3, pp. 1561-1578. doi: 10.2140/agt.2007.7.1561

[1] I Agol, Tameness of hyperbolic 3–manifolds

[2] D Calegari, D Gabai, Shrinkwrapping and the taming of hyperbolic 3–manifolds, J. Amer. Math. Soc. 19 (2006) 385

[3] D Gabai, Foliations and the topology of $3$-manifolds, J. Differential Geom. 18 (1983) 445

[4] A Marden, The geometry of finitely generated kleinian groups, Ann. of Math. $(2)$ 99 (1974) 383

[5] R Myers, End reductions, fundamental groups, and covering spaces of irreducible open 3–manifolds, Geom. Topol. 9 (2005) 971

[6] R Roussarie, Plongements dans les variétés feuilletées et classification de feuilletages sans holonomie, Inst. Hautes Études Sci. Publ. Math. (1974) 101

[7] J Stallings, On fibering certain $3$-manifolds, from: "Topology of 3–manifolds and related topics (Proc. The Univ. of Georgia Institute, 1961)" (editor M Fort), Prentice-Hall (1962) 95

[8] T W Tucker, Non-compact 3–manifolds and the missing-boundary problem, Topology 13 (1974) 267

[9] F Waldhausen, On irreducible 3–manifolds which are sufficiently large, Ann. of Math. $(2)$ 87 (1968) 56

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