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Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)

 

 

Imbedding free cyclic group actions in circle group actions


Author: Jeffrey L. Tollefson
Journal: Proc. Amer. Math. Soc. 26 (1970), 671-673
MSC: Primary 55.36; Secondary 57.00
DOI: https://doi.org/10.1090/S0002-9939-1970-0267580-1
MathSciNet review: 0267580
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Abstract: Suppose a closed, orientable, irreducible $ 3$-manifold $ M$ admits a free cyclic group action of prime order. We consider the problem of determining when $ M$ admits an effective action of the circle group $ SO(2)$ in which the cyclic action is imbedded. The main result is that if the $ {Z_k}$ action is ``$ Z$-classified", then it is weakly equivalent to a $ {Z_k}$ action imbedded in an effective action of $ SO(2)$ if and only if some homeomorphism generating the first $ {Z_k}$ action is homotopic to the identity homeomorphism on $ M$.


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DOI: https://doi.org/10.1090/S0002-9939-1970-0267580-1
Keywords: Finite cyclic group actions, $ 3$-manifolds, circle group actions
Article copyright: © Copyright 1970 American Mathematical Society