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Transactions of the American Mathematical Society

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

 

 

The complex bordism of groups with periodic cohomology


Authors: Anthony Bahri, Martin Bendersky, Donald M. Davis and Peter B. Gilkey
Journal: Trans. Amer. Math. Soc. 316 (1989), 673-687
MSC: Primary 55N22
DOI: https://doi.org/10.1090/S0002-9947-1989-0942423-8
MathSciNet review: 942423
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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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DOI: https://doi.org/10.1090/S0002-9947-1989-0942423-8
Keywords: Classifying spaces of finite groups, equivariant complex bordism, $ K$-theory, groups with periodic cohomology
Article copyright: © Copyright 1989 American Mathematical Society