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

 

On the bordism of almost free $ Z\sb{2k}$ actions


Author: R. Paul Beem
Journal: Trans. Amer. Math. Soc. 225 (1977), 83-105
MSC: Primary 57D85
MathSciNet review: 0425991
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Abstract: An ``almost free'' $ {Z_{{2^k}}}$ action on a manifold is one in which only the included $ {Z_2}$ may possibly fix points of the manifold. For k = 2, these are the stationary-point free actions. It is shown that almost free $ {Z_{{2^k}}}$ bordism is generated by three subalgebras: the extension from $ {Z_2}$ actions, a coset of $ {Z_2}$ extensions being the restrictions of circle actions and a certain ideal of elements which annihilate the whole ring. The additive structure is determined. Free $ {Z_{{2^k}}}$ bordism is shown to split as an algebra. It is shown that the kernel of the extension homomorphism from $ {Z_2}$ to $ {Z_{{2^k}}}$ bordism is equal to the image of the corresponding restriction homomorphism.


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Additional Information

DOI: http://dx.doi.org/10.1090/S0002-9947-1977-0425991-6
PII: S 0002-9947(1977)0425991-6
Keywords: Equivariant bordism
Article copyright: © Copyright 1977 American Mathematical Society