QUASI-REGULAR MAPS S-3-]S-3 WITH WILD BRANCH SETS

Two examples of quasiregular maps S-3-->S-3 that branch on a wild Cant or set are constructed. As an application it is shown that certain int eresting 3-dimensional metric spaces recently constructed by Semmes ad mit Lipschitz branched covers onto S-3. Moreover, it is shown that a u niformly quasiconformal group of Freedman and Skora acting on S-3 and not topologically conjugate to a Mobius group is quasiregularly semico njugate to a Mobius group. (C) 1997 Elsevier Science Ltd.