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3-variétes qui ne sont pas des revêtements cycliques ramifiés sur S3



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Montesinos Amilibia, José María (1975) 3-variétes qui ne sont pas des revêtements cycliques ramifiés sur S3. Proceedings of the American Mathematical Society, 47 . pp. 495-500. ISSN 0002-9939

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URL Oficial: http://www.ams.org/journals/proc/1975-047-02/S0002-9939-1975-0353293-9/S0002-9939-1975-0353293-9.pdf

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Let M denote a p-fold, branched, cyclic, covering space of S3, and suppose that the three-dimensional Smith conjecture is true for p-periodic autohomeomorphisms of S3. J. S. Birman and H. M. Hilden have constructed an algorithm for deciding whether M is homeomorphic to S3 [Bull. Amer. Math. Soc. 79 (1973), 1006–1010]. Now every closed, orientable three-manifold is a three-fold covering space of S3 branched over a knot [Hilden, ibid. 80 (1974), 1243–1244], but, in the present paper, the author shows that, if Fg is a closed, orientable surface of genus g≥1, then Fg×S1 is not a p-fold, branched cyclic covering space of S3 for any p. As the author points out, this was previously known for p=2 [R. H. Fox, Mat. Hisp.-Amer. (4) 32 (1972), 158–166; the author, Bol. Soc. Mat. Mexicana (2) 18 (1973), 1–32].

Tipo de documento:Artículo
Palabras clave:Cyclic branched covering spaces, three manifolds, three-sphere, two manifolds
Materias:Ciencias > Matemáticas > Topología
Código ID:17298
Depositado:03 Dic 2012 10:17
Última Modificación:07 Feb 2014 09:45

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