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oai:docta.ucm.es:20.500.14352/648422023-08-28T11:35:38Zcom_20.500.14352_14col_20.500.14352_15

Reducción de la conjetura de Poincaré a otras conjeturas geométricas Reduction of the Poincaré conjecture to other geometric conjectures Montesinos Amilibia, José María 515.1 Variedades orientables Recubridores ramificados Conjeturas geométricas Topología 1210 Topología Throughout 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. Depto. de Álgebra, Geometría y Topología Fac. de Ciencias Matemáticas TRUE pub 2023-06-21T02:05:52Z 2023-06-21T02:05:52Z 1972 journal article https://hdl.handle.net/20.500.14352/64842 0373-0999 spa restricted access application/pdf Real Sociedad Matemática Española; Consejo Superior de Investigaciones Científicas. Instituto "Jorge Juan" de Matemáticas