Representing open 3-manifolds as 3-fold branched coverings
| dc.contributor.author | Montesinos Amilibia, José María | |
| dc.date.accessioned | 2023-06-20T18:48:05Z | |
| dc.date.available | 2023-06-20T18:48:05Z | |
| dc.date.issued | 2002 | |
| dc.description.abstract | It is a celebrated result of H. Hilden and the author of the present paper that every closed, connected, oriented 3-manifold is a 3-fold irregular (dihedral) branched covering of the 3-sphere, branched over a knot. Here the author explores a generalization of this result to the case of non-compact manifolds. It is shown that a non-compact, connected, oriented 3-manifold is a 3-fold irregular branched covering of an open subspace of S3, branched over a locally finite family of proper arcs. The branched covering is constructed in such a way that it extends to a branched covering (suitably understood) of the Freudenthal end compactification over the entire 3-sphere. In particular all (uncountably many) contractible open 3-manifolds may be expressed as 3-fold branched coverings of R3, branched over a locally finite collection of proper arcs. | |
| 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/22287 | |
| dc.identifier.issn | 1139-1138 | |
| dc.identifier.officialurl | http://www.mat.ucm.es/serv/revmat/vol15-2j.html | |
| dc.identifier.relatedurl | http://www.springer.com/ | |
| dc.identifier.uri | https://hdl.handle.net/20.500.14352/58656 | |
| dc.issue.number | 2 | |
| dc.journal.title | Revista matemática complutense | |
| dc.language.iso | eng | |
| dc.page.final | 542 | |
| dc.page.initial | 533 | |
| dc.publisher | Springer | |
| dc.rights.accessRights | restricted access | |
| dc.subject.cdu | 515.162 | |
| dc.subject.keyword | 3-manifolds | |
| dc.subject.ucm | Topología | |
| dc.subject.unesco | 1210 Topología | |
| dc.title | Representing open 3-manifolds as 3-fold branched coverings | |
| dc.type | journal article | |
| dc.volume.number | 15 | |
| dcterms.references | Israel Berstein, Allan L. Edmonds, The degree and branch set of a branched covering. Invent. Math. 45 (1978) 213–220. Joan S. Birman, Hugh M. Hilden, The homeomorphism problem for S3. Bull. Amer. Math. Soc. 79 (1973) 1006–1010. E. M. Brown, T. W. Tucker, On proper homotopy theory for noncompact 3-manifolds. Trans. Amer. Math. Soc. 188 (1974) 105–126. Allan L. Edmonds, Branched coverings and orbit maps. Michigan Math. J. 23 (1976), 289–301. Ralph H. Fox, Covering spaces with singularities. 1957 A symposium in honor of S. Lefschetz pp. 243–257 Princeton University Press, Princeton, N.J. Ralph H. Fox, A note on branched cyclic covering of spheres. Rev. Mat. Hisp.-Amer. (4) 32 (1972) 158–166. Hans Freudenthal, Über die Enden diskreter Räume und Gruppen. Comment. Math. Helv. 17 (1945) 1–38. John Hempel, Construction of orientable 3-manifolds. 1962 Topology of 3-manifolds and related topics (Proc. The Univ. of Georgia Institute, 1961) pp. 207–212 Prentice-Hall, Englewood Cliffs, N.J. Hugh M. Hilden, Every closed orientable 3-manifold is a 2-fold branched covering space of S3. Bull. Amer. Math. Soc. 80 (1974) 1243–1244. Hugh M. Hilden, Three-fold branched coverings of S3. Amer. J. Math. 98 (1976), no. 4, 989–997. Jim Hoste, Framed link diagrams of open 3-manifolds. KNOTS '96 (Tokyo), 515–537, World Sci. Publishing, River Edge, NJ, 1997. Greg Kuperberg, A volume-preserving counterexample to the Seifert conjecture. Comment. Math. Helv. 71 (1996), no. 1, 70–97. W. B. R. Lickorish, A representation of orientable combinatorial 3-manifolds. Ann. of Math. (2) 76 (1962) 531–540. Edwin E. Moise, Affine structures in 3-manifolds. V. The triangulation theorem and Hauptvermutung. Ann. of Math. (2) 56 (1952) 96–114. Edwin E. Moise, Geometric topology in dimensions 2 and 3. Graduate Texts in Mathematics, Vol. 47. Springer-Verlag, New York-Heidelberg, 1977. x+262 pp. José M. Montesinos, A representation of closed orientable 3-manifolds as 3-fold branched coverings of S3. Bull. Amer. Math. Soc. 80 (1974) 845–846. José M. Montesinos, Three-manifolds as 3-fold branched covers of S3. Quart. J. Math. Oxford Ser. (2) 27 (1976), no. 105, 85–94. José M. Montesinos, A note on 3-fold branched coverings of S3 Math. Proc. Cambridge Philos. Soc. 88 (1980), no. 2, 321–325. José M. Montesinos, Open 3-manifolds as branched coverings. Rev. R. Acad. Cie. Serie A Mat. 95(2), (2001) 279–280. Andrew H. Wallace, Modifications and cobounding manifolds. Canad. J. Math. 12 (1960) 503–528. | |
| dspace.entity.type | Publication | |
| relation.isAuthorOfPublication | 7097502e-a5b0-4b03-b547-bc67cda16ae2 | |
| relation.isAuthorOfPublication.latestForDiscovery | 7097502e-a5b0-4b03-b547-bc67cda16ae2 |
Download
Original bundle
1 - 1 of 1