The complex bordism of groups with periodic cohomology

Bahri, Anthony; Bendersky, Martin; Davis, Donald M.; Gilkey, Peter B.

doi:10.1090/S0002-9947-1989-0942423-8

The complex bordism of groups with periodic cohomology
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by Anthony Bahri, Martin Bendersky, Donald M. Davis and Peter B. Gilkey

Trans. Amer. Math. Soc. 316 (1989), 673-687

DOI: https://doi.org/10.1090/S0002-9947-1989-0942423-8

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Abstract:

Is is proved that if $BG$ is the classifying space of a group $G$ with periodic cohomology, then the complex bordism groups $M{U_{\ast }}(BG)$ are obtained from the connective $K$-theory groups $k{u_{\ast }}(BG)$ by just tensoring up with the generators of $M{U_{\ast }}$ as a polynomial algebra over $k{u_{\ast }}$. The explicit abelian group structure is also given. The bulk of the work is the verification when $G$ is a generalized quaternionic group.

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The relation of cobordism to

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