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Transactions of the American Mathematical Society

ISSN 1088-6850(online) ISSN 0002-9947(print)



On the bordism of almost free $Z_{2k}$ 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 β€œalmost 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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Keywords: Equivariant bordism
Article copyright: © Copyright 1977 American Mathematical Society