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Revista Colombiana de Matemáticas
Print version ISSN 0034-7426
Rev.colomb.mat. vol.41 no.2 Bogotá July/Dec. 2007
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.
2000 Mathematics Subject Classification: 57M12, 57M30, 57N10, 54B15.
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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Este artículo se puede citar en LaTeX utilizando la siguiente referencia bibliográfica de BibTeX:
@ARTICLE{Montesinos-Amilibia07,
AUTHOR = {José María Montesinos-Amilibia},
TITLE = {{Open 3-manifolds and branched coverings: a quick exposition}},
JOURNAL = {Revista Colombiana de Matemáticas},
YEAR = {2007},
volume = {41},
number = {2},
pages = {287-302}
}