Representing 3-manifolds by a universal branching set
| dc.contributor.author | Montesinos Amilibia, José María | |
| dc.date.accessioned | 2023-06-21T02:02:47Z | |
| dc.date.available | 2023-06-21T02:02:47Z | |
| dc.date.issued | 1983-07 | |
| dc.description.abstract | The author shows that every compact connected oriented 3-manifold, after capping off boundary components by cones, is a covering of S3 branched over the 1-complex G which is "a pair of eyeglasses''. The author gives algorithms for passing between a Heegaard decomposition of a 3-manifold and this covering description. He also determines necessary and sufficient conditions for such a covering to have cone singularities. In a paper by W. Thurston ["Universal links'', Preprint], a link with similar properties (for closed 3-manifolds) to G is constructed. | |
| dc.description.department | Depto. de Álgebra, Geometría y Topología | |
| dc.description.faculty | Fac. de Ciencias Matemáticas | |
| dc.description.refereed | TRUE | |
| dc.description.sponsorship | Comisión Asesora del Ministerio de Educación y Ciencia | |
| dc.description.status | pub | |
| dc.eprint.id | https://eprints.ucm.es/id/eprint/17198 | |
| dc.identifier.doi | 10.1017/S0305004100060941 | |
| dc.identifier.issn | 0305-0041 | |
| dc.identifier.officialurl | http://journals.cambridge.org/abstract_S0305004100060941 | |
| dc.identifier.relatedurl | http://journals.cambridge.org/ | |
| dc.identifier.uri | https://hdl.handle.net/20.500.14352/64701 | |
| dc.issue.number | 1 | |
| dc.journal.title | Mathematical Proceedings of the Cambridge Philosophical Society | |
| dc.language.iso | eng | |
| dc.page.final | 123 | |
| dc.page.initial | 109 | |
| dc.publisher | Cambridge Univ Press | |
| dc.rights.accessRights | restricted access | |
| dc.subject.cdu | 515.16 | |
| dc.subject.keyword | branched coverings of the 3-sphere | |
| dc.subject.keyword | finite presentation of fundamental group | |
| dc.subject.keyword | compact | |
| dc.subject.keyword | connected | |
| dc.subject.keyword | oriented 3-manifold without 2-spheres in the boundary | |
| dc.subject.keyword | singular 3-manifold | |
| dc.subject.keyword | Heegaard diagram | |
| dc.subject.ucm | Topología | |
| dc.subject.unesco | 1210 Topología | |
| dc.title | Representing 3-manifolds by a universal branching set | |
| dc.type | journal article | |
| dc.volume.number | 94 | |
| dcterms.references | Alexander, J. W. Note on Riemann spaces. Bull. Amer. Math. Soc. 26 (1920), 370–372. Fox, R. H. Covering spaces with singularities. In Algebraic Geometry and Topology: a Symposium in Honor of S. Lefschetz (Princeton, 1957). Lyndon, R. C. & Schupp, P. E. Combinatorial group theory (Springer-Verlag 1977). Neuwirth, L. Knot groups. Ann. Math. Studies 56 (1965). Neuwirth, L. An algorithm for the construction of 3-manifolds from 2-complexes. Proc. Cambridge Philos. Soc. 64 (1968), 603–613 Poincaré, H. Cinquième complément à l'analysis situs. Rend. Circ. Mat. Palermo 18 (1904), 45–110. Ramírez, A. Sobre un teorema de Alexander. Anales del Instituto de Matemáticas UNAM 15 (1975), 77–81. Seifert, H. & Threlfall, W. A textbook of topology (Academic Press, 1980). Waldhausen, F. Some problems on 3-manifolds. Proceedings of Symposia in Pure Mathematics 32 (1978), 313–322. Whitehead, J. H. C. On certain sets of elements in a free group. Proc. London Math. Soc. 41 (1936), 48–56. | |
| dspace.entity.type | Publication | |
| relation.isAuthorOfPublication | 7097502e-a5b0-4b03-b547-bc67cda16ae2 | |
| relation.isAuthorOfPublication.latestForDiscovery | 7097502e-a5b0-4b03-b547-bc67cda16ae2 |
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