For each 1 <= p < 2, there exist orientation-preserving and orientation-reversing wild involutions of S^3 in the Sobolev class W^{1,p}(S^3,S^3).
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For each 1 <= p < 2, there exist orientation-preserving and orientation-reversing wild involutions of S^3 in the Sobolev class W^{1,p}(S^3,S^3).