Lectures on 3-fold simple coverings and 3-manifolds
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 c...
| Autor: | |
|---|---|
| Tipo de recurso: | capítulo de libro |
| Fecha de publicación: | 1985 |
| País: | España |
| Institución: | Universidad Complutense de Madrid (UCM) |
| Repositorio: | Docta Complutense |
| Idioma: | inglés |
| OAI Identifier: | oai:docta.ucm.es:20.500.14352/65466 |
| Acceso en línea: | https://hdl.handle.net/20.500.14352/65466 |
| Access Level: | acceso abierto |
| Palabra clave: | 515.1 3-manifolds as branched coverings of the 3-sphere surfaces as branched covers of S 2 Dehn surgery simple covers coloured links Poincaré conjecture parallelizable Topología 1210 Topología |
| id |
ES_b641078e5cc7785977a0d8aafc73ebfb |
|---|---|
| oai_identifier_str |
oai:docta.ucm.es:20.500.14352/65466 |
| network_acronym_str |
ES |
| network_name_str |
España |
| repository_id_str |
|
| spelling |
Lectures on 3-fold simple coverings and 3-manifoldsMontesinos Amilibia, José María515.13-manifolds as branched coverings of the 3-spheresurfaces as branched covers of S 2Dehn surgerysimple coverscoloured linksPoincaré conjectureparallelizableTopología1210 TopologíaThe 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 Ω: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.American Mathematical SocietyHarper, John R.Mandelbaum, RichardUniversidad Complutense de Madrid19851985-01-0119851985-01-01book parthttp://purl.org/coar/resource_type/c_3248info:eu-repo/semantics/bookPartapplication/pdfhttps://hdl.handle.net/20.500.14352/65466reponame:Docta Complutenseinstname:Universidad Complutense de Madrid (UCM)Inglésengopen accesshttp://purl.org/coar/access_right/c_abf2info:eu-repo/semantics/openAccessoai:docta.ucm.es:20.500.14352/654662026-06-02T12:44:21Z |
| dc.title.none.fl_str_mv |
Lectures on 3-fold simple coverings and 3-manifolds |
| title |
Lectures on 3-fold simple coverings and 3-manifolds |
| spellingShingle |
Lectures on 3-fold simple coverings and 3-manifolds Montesinos Amilibia, José María 515.1 3-manifolds as branched coverings of the 3-sphere surfaces as branched covers of S 2 Dehn surgery simple covers coloured links Poincaré conjecture parallelizable Topología 1210 Topología |
| title_short |
Lectures on 3-fold simple coverings and 3-manifolds |
| title_full |
Lectures on 3-fold simple coverings and 3-manifolds |
| title_fullStr |
Lectures on 3-fold simple coverings and 3-manifolds |
| title_full_unstemmed |
Lectures on 3-fold simple coverings and 3-manifolds |
| title_sort |
Lectures on 3-fold simple coverings and 3-manifolds |
| dc.creator.none.fl_str_mv |
Montesinos Amilibia, José María |
| author |
Montesinos Amilibia, José María |
| author_facet |
Montesinos Amilibia, José María |
| author_role |
author |
| dc.contributor.none.fl_str_mv |
Harper, John R. Mandelbaum, Richard Universidad Complutense de Madrid |
| dc.subject.none.fl_str_mv |
515.1 3-manifolds as branched coverings of the 3-sphere surfaces as branched covers of S 2 Dehn surgery simple covers coloured links Poincaré conjecture parallelizable Topología 1210 Topología |
| topic |
515.1 3-manifolds as branched coverings of the 3-sphere surfaces as branched covers of S 2 Dehn surgery simple covers coloured links Poincaré conjecture parallelizable Topología 1210 Topología |
| description |
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 Ω: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. |
| publishDate |
1985 |
| dc.date.none.fl_str_mv |
1985 1985-01-01 1985 1985-01-01 |
| dc.type.none.fl_str_mv |
book part http://purl.org/coar/resource_type/c_3248 |
| dc.type.openaire.fl_str_mv |
info:eu-repo/semantics/bookPart |
| format |
bookPart |
| dc.identifier.none.fl_str_mv |
https://hdl.handle.net/20.500.14352/65466 |
| url |
https://hdl.handle.net/20.500.14352/65466 |
| dc.language.none.fl_str_mv |
Inglés eng |
| language_invalid_str_mv |
Inglés |
| language |
eng |
| dc.rights.none.fl_str_mv |
open access http://purl.org/coar/access_right/c_abf2 |
| dc.rights.openaire.fl_str_mv |
info:eu-repo/semantics/openAccess |
| rights_invalid_str_mv |
open access http://purl.org/coar/access_right/c_abf2 |
| eu_rights_str_mv |
openAccess |
| dc.format.none.fl_str_mv |
application/pdf |
| dc.publisher.none.fl_str_mv |
American Mathematical Society |
| publisher.none.fl_str_mv |
American Mathematical Society |
| dc.source.none.fl_str_mv |
reponame:Docta Complutense instname:Universidad Complutense de Madrid (UCM) |
| instname_str |
Universidad Complutense de Madrid (UCM) |
| reponame_str |
Docta Complutense |
| collection |
Docta Complutense |
| repository.name.fl_str_mv |
|
| repository.mail.fl_str_mv |
|
| _version_ |
1869417431416438784 |
| score |
15,300719 |