Vector bundles over finite 𝐶𝑊-complexes are algebraic

Lønsted, Knud

doi:10.1090/S0002-9939-1973-0317315-1

Vector bundles over finite $\textrm {CW}$-complexes are algebraic
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Proc. Amer. Math. Soc. 38 (1973), 27-31 Request permission

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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