Open 3-manifolds, wild subsets of S3 and branched coverings
| dc.contributor.author | Montesinos Amilibia, José María | |
| dc.date.accessioned | 2023-06-20T18:48:08Z | |
| dc.date.available | 2023-06-20T18:48:08Z | |
| dc.date.issued | 2003 | |
| dc.description.abstract | It is proved that any closed orientable 3-manifold is a 3-fold irregular branched covering of the 3-sphere branched over a wildly embedded knot. These branched coverings are obtained by starting with such a branched covering over a tame knot and then inserting into it a particular irregular branched covering of the 3-sphere over the 3-sphere, with a wild branch set. It is also shown how to use related techniques to produce branched coverings of certain open 3-manifolds over tame, properly embedded arcs in R3. For example, the Whitehead contractible open 3-manifold is expressible as a 2-fold branched covering over such an arc, conjecturally in uncountably many different ways. These results should be considered as illustrations of the general construction given in the author's recent paper [Rev. Mat. Complut. 15 (2002), no. 2, 533–542 | |
| dc.description.department | Depto. de Álgebra, Geometría y Topología | |
| dc.description.faculty | Fac. de Ciencias Matemáticas | |
| dc.description.refereed | TRUE | |
| dc.description.status | pub | |
| dc.eprint.id | https://eprints.ucm.es/id/eprint/22292 | |
| dc.identifier.issn | 1139-1138 | |
| dc.identifier.officialurl | http://www.mat.ucm.es/serv/revmat/vol16-2m.html | |
| dc.identifier.relatedurl | http://www.springer.com/ | |
| dc.identifier.uri | https://hdl.handle.net/20.500.14352/58659 | |
| dc.issue.number | 2 | |
| dc.journal.title | Revista matemática complutense | |
| dc.language.iso | eng | |
| dc.page.final | 600 | |
| dc.page.initial | 577 | |
| dc.publisher | Springer | |
| dc.rights.accessRights | restricted access | |
| dc.subject.cdu | 515.162 | |
| dc.subject.keyword | Wild knots | |
| dc.subject.keyword | open manifolds | |
| dc.subject.keyword | branched coverings. | |
| dc.subject.ucm | Topología | |
| dc.subject.unesco | 1210 Topología | |
| dc.title | Open 3-manifolds, wild subsets of S3 and branched coverings | |
| dc.type | journal article | |
| dc.volume.number | 16 | |
| dcterms.references | Burde, Gerhard; Zieschang, Heiner. Knots. De Gruyter Studies in Mathematics, 5. Berlin - New York: Walter de Gruyter. XII, 399 p. (1985). Brown, Morton. The monotone union of open n-cells is an open n-cell. Proc. Amer. Math. Soc. 12 (1961) 812–814. Fox, Ralph H. Covering spaces with singularities. 1957 A symposium in honor of S. Lefschetz pp. 243–257 Princeton University Press, Princeton, N.J. Fox, Ralph H. A remarkable simple closed curve. Ann. of Math. (2) 50, (1949). 264–265. Freudenthal, Hans. Über die Enden diskreter Räume und Gruppen. Comment. Math. Helv. 17 (1945) 1–38. Hilden, Hugh M. Every closed orientable 3-manifold is a 2-fold branched covering space of S3. Bull. Amer. Math. Soc. 80 (1974) 1243–1244. Hilden, Hugh M. Three-fold branched coverings of S3. Amer. J. Math. 98 (1976), no. 4, 989–997. Hilden, Hugh M.; Lozano, María Teresa; Montesinos-Amilibia, José María. On the character variety of periodic knots and links. Math. Proc. Camb. Philos. Soc. 129, No.3, 477–490 (2000). Hoste, Jim Framed link diagrams of open 3-manifolds. KNOTS `96 (Tokyo), 515–537, World Sci. Publishing, River Edge, NJ, 1997. Montesinos-Amilibia, José María. A representation of closed orientable 3-manifolds as 3-fold branched coverings of S3. Bull. Amer. Math. Soc. 80 (1974) 845–846. Montesinos-Amilibia, José María. Three-manifolds as 3-fold branched covers of S3. Quart. J. Math. Oxford Ser. (2) 27 (1976), no. 105, 85–94. Montesinos-Amilibia, José María. Open 3-manifolds as 3-fold branched coverings. Rev.R.Acad.Cien.SerieA.Mat. 95(2001)1–3. Montesinos-Amilibia, José María. Representing open 3-manifolds as 3-fold branched coverings, Revista Matemática Complutense, 15 (2002) 533–542. Schubert, Horst Knoten mit zwei Brücken. Math. Z. 65, 133–170 (1956). Whitehead, J.H.C A certain region in Euclidean 3-space. Proc. Natl. Acad. Sci. USA 21, 364–366 (1935). | |
| dspace.entity.type | Publication | |
| relation.isAuthorOfPublication | 7097502e-a5b0-4b03-b547-bc67cda16ae2 | |
| relation.isAuthorOfPublication.latestForDiscovery | 7097502e-a5b0-4b03-b547-bc67cda16ae2 |
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