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Open 3-manifolds, wild subsets of S and branched coverings.

José María Montesinos-Amilibia — 2003

Revista Matemática Complutense

In this paper, a representation of closed 3-manifolds as branched coverings of the 3-sphere, proved in [13], and showing a relationship between open 3-manifolds and wild knots and arcs will be illustrated by examples. It will be shown that there exist a 3-fold simple covering p : S --> S branched over the remarkable simple closed curve of Fox [4] (a wild knot). Moves are defined such that when applied to a branching set, the corresponding covering manifold remains unchanged, while the branching...

The Whitehead link, the Borromean rings and the knot 9 are universal.

Hugh M. HildenMaría Teresa LozanoJosé María Montesinos — 1983

Collectanea Mathematica

A link L in S is universal if every closed, orientable 3-manifold is a covering of S branched over L. Thurston [1] proved that universal links exist and he asked if there is a universal knot, and also if the Whitehead link and the Figure-eight knot are universal. In [2], [3] we answered the first question by constructing a universal knot. The purpose of this paper is to prove that the Whitehead link and the Borromean rings, among others, are universal. The question about the Figure-eight knot remains...

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