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Uncountably many wild knots whose cyclic branched covering are S3

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Montesinos Amilibia, José María (2003) Uncountably many wild knots whose cyclic branched covering are S3. Revista matemática complutense, 16 (1). pp. 329-344. ISSN 1139-1138

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Official URL: http://www.mat.ucm.es/serv/revmat/vol16-1j.html


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Abstract

According to the confirmed Smith Conjecture [The Smith conjecture (New York, 1979), Academic Press, Orlando, FL, 1984;], a tame knot in the 3-sphere has a cyclic branched covering that is also the 3-sphere only if it is trivial. Here the author produces a nontrivial, wild knot whose n-fold cyclic branched cover is S3, for all n. In fact there are uncountably many inequivalent knots with this property, and the knots can be chosen to bound an embedded disk that is tame in its interior. One might conjecture that any wild knot whose nontrivial n-fold cyclic branched cover is S3 must bound such a disk that is tame in its interior.


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Dedicado a Francisco González Acuña en su sexagésimo cumpleaños

Uncontrolled Keywords:decomposition, wild knot, branched covering
Subjects:Sciences > Mathematics > Topology
ID Code:22293
Deposited On:09 Jul 2013 17:13
Last Modified:12 Dec 2018 15:13

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