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Open 3-manifolds, wild subsets of S3 and branched coverings

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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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Official URL: http://www.mat.ucm.es/serv/revmat/vol16-2m.html


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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
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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