There is a disk in S3 whose interior is PL embedded and whose boundary has a tame Cantor set of locally wild points, such that the n-fold cyclic coverings of S3 branched over the boundary of the disk are all S3. An uncountable set of inequivalent wild knots with these properties is exhibited.
@article{urn:eudml:doc:44432, title = {Uncountably many wild knots whose cyclic branched covering are S3.}, journal = {Revista Matem\'atica de la Universidad Complutense de Madrid}, volume = {16}, year = {2003}, pages = {329-344}, zbl = {1052.57015}, mrnumber = {MR2031886}, language = {en}, url = {http://dml.mathdoc.fr/item/urn:eudml:doc:44432} }
Montesinos-Amilibia, José María. Uncountably many wild knots whose cyclic branched covering are S3.. Revista Matemática de la Universidad Complutense de Madrid, Tome 16 (2003) pp. 329-344. http://gdmltest.u-ga.fr/item/urn:eudml:doc:44432/