Abstract

MONTESINOS-AMILIBIA, JOSÉ MARÍA. Open 3-manifolds and branched coverings: a quick exposition. Rev.colomb.mat. [online]. 2007, vol.41, n.2, pp.287-302. ISSN 0034-7426.

Branched coverings relate closed, orientable 3-manifolds to links in S³, and open, orientable 3-manifolds to strings in S³\smallsetminus T, where T is a compact, totally disconnected tamely embedded subset of S³. Here we give the foundations of this last relationship. We introduce Fox theory of branched coverings and state the main theorems. We give examples to illustrate the theorems.

Keywords : Knot; link; manifold; string; wild; tame; locally tame; Cantor set; tangle; branched covering; colored knot; Smith conjecture.

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