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Reducción de la conjetura de Poincaré a otras conjeturas geométricas

dc.contributor.authorMontesinos Amilibia, José María
dc.date.accessioned2023-06-21T02:05:52Z
dc.date.available2023-06-21T02:05:52Z
dc.date.issued1972
dc.description.abstractThroughout his paper, the author uses "orientable manifold'' to mean a compact connected orientable 3-manifold without boundary. Such a manifold is known to be a ramified covering over a link of the 3-sphere, in which the ramification index of each singular point is ≤2. If the covering has n leaves, suppose that there are m points of index 2 and 2m points of index 1; such a covering is of type (m,n−2m). The author's main theorem states: Every orientable manifold is a ramified covering of type (1,n−2). He also uses the notion of a "link with a colouring of type (m,n−2m)''; these are intimately related to ramified coverings of type (m,n−2m). He conjectures that every link having a colouring of type (1,n−2) is "separable'', a term too complicated to define here. With this conjecture and his main theorem, he enunciates two further theorems and a second conjecture to show that his two conjectures, if true, would imply the Poincaré hypothesis for 3-manifolds. The author adds a note in proof to say that his first conjecture is false, as will be shown in a forthcoming paper by R. H. Fox. It therefore seems unnecessary to detail the conjectures in this review.
dc.description.departmentDepto. de Álgebra, Geometría y Topología
dc.description.facultyFac. de Ciencias Matemáticas
dc.description.refereedTRUE
dc.description.statuspub
dc.eprint.idhttps://eprints.ucm.es/id/eprint/21876
dc.identifier.issn0373-0999
dc.identifier.urihttps://hdl.handle.net/20.500.14352/64842
dc.journal.titleRevista Matemática Hispanoamericana
dc.language.isospa
dc.page.final51
dc.page.initial33
dc.publisherReal Sociedad Matemática Española; Consejo Superior de Investigaciones Científicas. Instituto "Jorge Juan" de Matemáticas
dc.rights.accessRightsrestricted access
dc.subject.cdu515.1
dc.subject.keywordVariedades orientables
dc.subject.keywordRecubridores ramificados
dc.subject.keywordConjeturas geométricas
dc.subject.ucmTopología
dc.subject.unesco1210 Topología
dc.titleReducción de la conjetura de Poincaré a otras conjeturas geométricas
dc.title.alternativeReduction of the Poincaré conjecture to other geometric conjectures
dc.typejournal article
dc.volume.number32
dcterms.references[l] J. W. ALEXANDER: Note on Riemann spaces. «Bull. Amer. Math. Soc.», 26 (1920), 370-372. [2] W. CLIFFORD: On the canonical form and dissection of a Riemann's surface. «Proc. London Math. Soc.», 8 (1877), 292-304. [3] R. H. CROWELL & R. H. FOX: An introduction to Knot Theory. Gin & Company [4] R. H. FOX: Covering spaces with singularities. «Algebraic Geometry and Topology», A symposium in honour of S. Lefschetz. Princeton, 1957. [5] -- Construction of simply connected 3-manifolds. Topology of 3-manifolds and related topics, Englewood Cliffs N. J. (1962), Prentice Hall, 213-216. [6] -- A note on branched cyclic coverings of spheres (se publicará en «Revista Matemática Hispano-Americana»). [7] W. HAKEN: Some results on surfaces in 3-manifolds. «M. A. A. Studies in Mathematics», vol. 5. Studies in modern Topology, P. J. Hilton, editor, 39-98. [8] J. M. MONTESINOS: Sobre la conjetura de Poincaré y los recubridores ramificados sobre un nudo. Tesis Doctoral (será publicada en Departamento de Publicaciones de la Facultad de Ciencias de la Universidad de Madrid) (1971). [9] L. P. NEUWIRTH: Knots Groups. «Annal. of Math. Studies», núm. 56. [10] K. REIDEMEISTER: Knotentheorie, «Erg. d. Math.», 1, núm. 1, reimpreso Chelsea, N. 4. 1948. [ll] H. SEIFERT y THRELFALL: Lehrbuch der Topology. Leipzig und Berlin (1934). [12] F. WALDHAUSEN: Uber Involutionen de 3-Sphare. «Topology», 8 (1969), 81-91
dspace.entity.typePublication
relation.isAuthorOfPublication7097502e-a5b0-4b03-b547-bc67cda16ae2
relation.isAuthorOfPublication.latestForDiscovery7097502e-a5b0-4b03-b547-bc67cda16ae2

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