Reducción de la conjetura de Poincaré a otras conjeturas geométricas

dc.contributor.authorMontesinos Amilibia, José María
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
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dc.journal.titleRevista Matemática Hispanoamericana
dc.publisherReal Sociedad Matemática Española; Consejo Superior de Investigaciones Científicas. Instituto "Jorge Juan" de Matemáticas
dc.rights.accessRightsrestricted access
dc.subject.keywordVariedades orientables
dc.subject.keywordRecubridores ramificados
dc.subject.keywordConjeturas geométricas
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
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