On the bordism of almost free 𝑍_{2𝑘} actions

Beem, R. Paul

doi:10.1090/S0002-9947-1977-0425991-6

On the bordism of almost free $Z_{2k}$ actions
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Trans. Amer. Math. Soc. 225 (1977), 83-105 Request permission

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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