Abstract
This paper is devoted to the problem of classifying periodic homeomorphisms which act freely on the 3 3 -sphere. The main result is the classification of free period eight actions and a generalization to free actions whose squares are topologically equivalent to orthogonal transformations. The result characterizes those 3 3 -manifolds which have the 3 3 -sphere as universal covering space and the cyclic group of order eight as fundamental group.
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