Representing open 3-manifolds as 3-fold branched coverings

Résumé

It is proved that the Freudenthal compacti_cation of an open, connected, oriented 3-manifold is a 3-fold branched covering of S3, and in some cases, a 2-fold branched covering of S3:The branching set is a locally _nite disjoint union of strings. La compacti_caci_on de Freudenthal de una 3-variedad abierta conexa y orientable es una cubierta de 3 hojas rami_cada sobre S3 y, en ciertos casos, de dos hojas. La rami_caci_on es una uni_on localmente _nita y disjunta de cuerdas.