Montesinos Amilibia, José María (1975) Corrigendum to “3-variétés qui ne sont pas des revêtements cycliques ramifiés sur S 3". Proceedings of the American Mathematical Society, 53 . p. 541. ISSN 0002-9939
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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].
|Uncontrolled Keywords:||Cyclic branched covering spaces, three manifolds, three-sphere, two manifolds|
|Subjects:||Sciences > Mathematics > Topology|
|Deposited On:||03 Dec 2012 10:19|
|Last Modified:||07 Feb 2014 09:45|
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