Open 3-manifolds and branched coverings: a quick exposition.
Una nueva clasificación de automorfismos en un espacio vectorial.
Open 3-manifolds, wild subsets of S and branched coverings.
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...
Uncountably many wild knots whose cyclic branched covering are S.
There is a disk in S whose interior is PL embedded and whose boundary has a tame Cantor set of locally wild points, such that the n-fold cyclic coverings of S branched over the boundary of the disk are all S. An uncountable set of inequivalent wild knots with these properties is exhibited.
Representing open 3-manifolds as 3-fold branched coverings.
It is proved that the Freudenthal compactification of an open, connected, oriented 3-manifold is a 3-fold branched covering of S, and in some cases, a 2-fold branched covering of S. The branching set is a locally finite disjoint union of strings.
Around the Borromean link.
This is a survey of some consequences of the fact that the fundamental group of the orbifold with singular set the Borromean link and isotropy cyclic of order 4 is a universal kleinian group.
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