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Proceedings of the American Mathematical Society

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

 

 

Free actions of cyclic groups of order $ 2\sp{n}$ on $ S\sp{1}\times S\sp{2}$


Author: Gerhard X. Ritter
Journal: Proc. Amer. Math. Soc. 46 (1974), 137-140
MSC: Primary 57E25
MathSciNet review: 0350768
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Abstract: In [4] Y. Tao proved that if $ h$ is a fixed point free involution of $ {S^1} \times {S^2}$, then $ ({S^1} \times {S^2})/h$ must be homeomorphic to either $ {M_1} = {S^1} \times {S^2}$, or $ {M_2} = {{\mathbf{K}}^3}$, or $ {M_3} = {S^1} \times {{\mathbf{P}}^2}$ or $ {M_4} = {{\mathbf{P}}^3}\char93 {{\mathbf{P}}^3}$. In this paper we extend this result to free actions of $ {Z_{{2^n}}}$ on $ {S^1} \times {S^2}$, showing that, for $ n > 1,({S^1} \times {S^2})/{Z_{{2^n}}}$ must be homeomorphic to either $ {M_1}$ or $ {M_2}$.


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DOI: https://doi.org/10.1090/S0002-9939-1974-0350768-2
Keywords: Free actions, piecewise linear, polyhedral, isotopic, manifold
Article copyright: © Copyright 1974 American Mathematical Society