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Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)

 

 

Vector bundles over finite $ {\rm CW}$-complexes are algebraic


Author: Knud Lønsted
Journal: Proc. Amer. Math. Soc. 38 (1973), 27-31
MSC: Primary 55B15; Secondary 13D15
DOI: https://doi.org/10.1090/S0002-9939-1973-0317315-1
MathSciNet review: 0317315
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Abstract: It is proved that for any finite CW-complex $ X$ there exists a ring $ A$ of continuous functions on $ X$, and natural 1-1 correspondences between the finitely generated projective $ A$-modules (resp. $ A{ \otimes _R}C$-modules), and the topological real vector bundles (resp. complex vector bundles) over $ X$ where $ A$ is Noetherian and has Krull-dimension equal to the topological dimension of $ X$.


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Additional Information

DOI: https://doi.org/10.1090/S0002-9939-1973-0317315-1
Keywords: Vector bundles, topological $ K$-theory, algebraic $ K$-theory, finite CW-complexes, real analytic functions
Article copyright: © Copyright 1973 American Mathematical Society