Some aspects of the theory of branched coverings. (Spanish: Algunos aspectos de la teoría de cubiertas ramificadas)

Abstract

From the text: "We deal with coverings of the 3-sphere S3branched over a link (= a system of knots) as a way of representing closed orientable 3-manifolds. A simplicial mapping f:Mn→Nn between two compact triangulated n-manifolds M and N is called a branched covering if it is an ordinary covering outside of the (n−2)-skeleton of Nn. The points of Nn whose preimages have fewer points than the covering has leaves form a subcomplex Bn−2 called the branch locus. We use the phrase `f is a covering of Nn branched over B'. "Because this is an expository article, we deal only with some selected topics that help to give an idea of the theory. The material is generally known, although some results are new.''