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Transactions of the American Mathematical Society
Transactions of the American Mathematical Society
ISSN 1088-6850(online) ISSN 0002-9947(print)

 

Free $ Z\sb{8}$ actions on $ S\sp{3}$


Author: Gerhard X. Ritter
Journal: Trans. Amer. Math. Soc. 181 (1973), 195-212
MSC: Primary 55C35; Secondary 57A10
MathSciNet review: 0321078
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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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Additional Information

DOI: http://dx.doi.org/10.1090/S0002-9947-1973-0321078-8
PII: S 0002-9947(1973)0321078-8
Keywords: Three-sphere, free action, orthogonal $ (p,q)$-action, knot, lens space, general position, topologically equivalent
Article copyright: © Copyright 1973 American Mathematical Society