¹Universidad Complutense, Madrid, España. Email: montesin@mat.ucm.es

Branched coverings relate closed, orientable 3-manifolds to links in S³, and open, orientable 3-manifolds to strings in S³\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.

Key words: Knot, link, manifold, string, wild, tame, locally tame, Cantor set, tangle, branched covering, colored knot, Smith conjecture.

Las cubiertas ramificadas relacionan las 3-variedades orientables cerradas con los enlaces en S³ y las 3-variedades abiertas con las cuerdas en S³\T, donde T es un subconjunto compacto, totalmente desconectado y dócilmente encajado en S³. Aquí exponemos los fundamentos básicos de esta última relación. Introducimos la teoría de Fox de las cubiertas ramificadas y enunciamos los principales teoremas. Damos ejemplos que ilustran los teoremas.

Palabras clave: Nudo, enlace, variedad, cuerda, salvaje, dócil, localmente dócil, conjunto de Cantor, ovillo, conjetura de Smith.

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