Título: | Lectures on 3-fold simple coverings and 3-manifolds |
Autores: | Montesinos Amilibia, José María |
Tipo de documento: | texto impreso |
Editorial: | American Mathematical Society, 1985 |
Dimensiones: | application/pdf |
Nota general: | info:eu-repo/semantics/openAccess |
Idiomas: | |
Palabras clave: | Estado = Publicado , Materia = Ciencias: Matemáticas: Topología , Tipo = Sección de libro |
Resumen: |
The author presents various ideas, proofs, constructions and tricks connected with branched coverings of 3-manifolds. After an introductory section on 2-fold branched coverings of S3 the main theme of 3-fold irregular coverings is introduced. A short proof is given of the Montesinos-Hilden theorem concerning the presentation of a (closed, oriented) 3-manifold as an irregular 3-fold covering of S3. Coloured links, associated with irregular 3-fold coverings, are discussed, and moves on coloured links which do not alter the associated covering. The last section contains an elegant proof of a theorem of Hilden and the author: Every closed oriented 3-manifold is a simple 3-fold covering of S3 branched over a knot so that the branching cover bounds an embedded disc. A consequence of this is the fact that every such 3-manifold is parallelizable. Finally the following result of H. M. Hilden , M. T. Lozano and the author [Trans. Amer. Math. Soc. 279 (1983), no. 2, 729–735;] is proved: Every closed oriented 3-manifold is the pullback of any 3-fold simple branched covering p:S3?S3 and some smooth map ?:S3?S3 transversal to the branching set of p. This implies an earlier result of Hilden: the possibility to embed any closed oriented 3-manifold M in S3×D2 so that the composition with the projection in the first factor is a 3-fold simple covering. |
En línea: | https://eprints.ucm.es/id/eprint/22069/7/Montesinos100.pdf |
Ejemplares
Estado |
---|
ningún ejemplar |