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 | References | Similar Articles | Additional Information
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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Additional Information
Keywords:
Finite cyclic group actions,
<IMG WIDTH="16" HEIGHT="20" ALIGN="BOTTOM" BORDER="0" SRC="images/img1.gif" ALT="$3$">-manifolds,
circle group actions
Article copyright:
© Copyright 1970
American Mathematical Society