Abstract
Two examples of quasiregular maps S 3 → S 3 that branch on a wild Cantor set are constructed. As an application it is shown that certain interesting 3-dimensional metric spaces recently constructed by Semmes admit Lipschitz branched covers onto S 3. Moreover, it is shown that a uniformly quasiconformal group of Freedman and Skora acting on S 3 and not topologically conjugate to a Möbius group is quasiregularly semiconjugate to a Möbius group.
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