Free 𝑍₈ actions on 𝑆³

Ritter, Gerhard X.

doi:10.1090/S0002-9947-1973-0321078-8

Free $Z_{8}$ actions on $S^{3}$
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by Gerhard X. Ritter

Trans. Amer. Math. Soc. 181 (1973), 195-212

DOI: https://doi.org/10.1090/S0002-9947-1973-0321078-8

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Abstract:

This paper is devoted to the problem of classifying periodic homeomorphisms which act freely on the $3$-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 $3$-manifolds which have the $3$-sphere as universal covering space and the cyclic group of order eight as fundamental group.

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Homotopieringe und Linsenräume

11

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Lehrbuch der Topologie

Seminar on combinatorial topology