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oai:docta.ucm.es:20.500.14352/586602023-08-25T23:04:19Zcom_20.500.14352_14col_20.500.14352_15

00925njm 22002777a 4500 dc Montesinos Amilibia, José María author 2003 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. 1139-1138 https://hdl.handle.net/20.500.14352/58660 http://www.mat.ucm.es/serv/revmat/vol16-1j.html http://www.springer.com/ Uncountably many wild knots whose cyclic branched covering are S3