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Strange actions of groups on spheres. (English) Zbl 0588.57024
For r sufficiently large we construct actions of generalized dihedral groups (free of rank r)\(\rtimes {\mathbb{Z}}_ 2\) on \(S^ 3\) which are discrete, smooth, uniformly quasiconformal, but which are not topologically conjugate to conformal actions. This is at odds with the situation for actions on \(S^ 2\). This and other wild analogs of Schottky actions are considered.

MSC:
57S25 Groups acting on specific manifolds
57S20 Noncompact Lie groups of transformations
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