Open 3-manifolds and branched coverings: a quick exposition

Abstract

This is a survey article discussing the author's work in a series of several publications on the relationship between 3-manifolds and wild knots in the 3-sphere and strings in R3 given by branched coverings. He includes an introduction to ordinary combinatorial branched coverings and a parallel introduction to the general topological branched coverings defined by R. H. Fox. Among other things one may conclude that every closed, oriented 3-manifold is a 3-fold covering of the 3-sphere branched over a wild knot. The paper ends with a brief discussion of two open problems.