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On the reduction of complex bordism to unoriented bordism


Author: David Copeland Johnson
Journal: Proc. Amer. Math. Soc. 39 (1973), 417-420
MSC: Primary 55B20
DOI: https://doi.org/10.1090/S0002-9939-1973-0322853-1
MathSciNet review: 0322853
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Abstract: The image of the natural transformation from the complex bordism of a CW complex $ X,M{U_ \ast }(X)$, to its unoriented bordism, $ {N_ \ast }(X)$, is contained in a subgroup identified with $ {H_ \ast }(X;Z) \otimes {({N_ \ast })^2}$. A characterization is given for the CW complexes for which the image and the subgroup coincide.


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DOI: https://doi.org/10.1090/S0002-9939-1973-0322853-1
Keywords: Complex bordism, unoriented bordism, projective dimension
Article copyright: © Copyright 1973 American Mathematical Society

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