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Montesinos Amilibia, José María (2003) Open 3-manifolds, wild subsets of S3 and branched coverings. Revista matemática complutense, 16 (2). pp. 577-600. ISSN 1139-1138
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Abstract
It is proved that any closed orientable 3-manifold is a 3-fold irregular branched covering of the 3-sphere branched over a wildly embedded knot. These branched coverings are obtained by starting with such a branched covering over a tame knot and then inserting into it a particular irregular branched covering of the 3-sphere over the 3-sphere, with a wild branch set. It is also shown how to use related techniques to produce branched coverings of certain open 3-manifolds over tame, properly embedded arcs in R3. For example, the Whitehead contractible open 3-manifold is expressible as a 2-fold branched covering over such an arc, conjecturally in uncountably many different ways. These results should be considered as illustrations of the general construction given in the author's recent paper [Rev. Mat. Complut. 15 (2002), no. 2, 533–542
Item Type: | Article |
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Uncontrolled Keywords: | Wild knots, open manifolds, branched coverings. |
Subjects: | Sciences > Mathematics > Topology |
ID Code: | 22292 |
Deposited On: | 09 Jul 2013 17:15 |
Last Modified: | 12 Dec 2018 15:13 |
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