Projective modules as fiber bundles
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- by E. Graham Evans
- Proc. Amer. Math. Soc. 27 (1971), 623-626
- DOI: https://doi.org/10.1090/S0002-9939-1971-0269642-2
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Abstract:
Projective modules over real affine rings, $R$, with compact real points, $X$, can be considered as fiber bundles over $X$ by tensoring with the real valued continuous functions on $X$. This induces a map $f:{K_0}(R) \to {K^0}(X)$, In this article the kernel of $f$ is determined and an example with nonzero kernel is given.References
- Robert M. Fossum, Vector bundles over spheres are algebraic, Invent. Math. 8 (1969), 222–225. MR 250298, DOI 10.1007/BF01406073
- R. G. Swan, Algebraic $K$-theory, Lecture Notes in Mathematics, No. 76, Springer-Verlag, Berlin-New York, 1968. MR 0245634
- Richard G. Swan, Vector bundles and projective modules, Trans. Amer. Math. Soc. 105 (1962), 264–277. MR 143225, DOI 10.1090/S0002-9947-1962-0143225-6
Bibliographic Information
- © Copyright 1971 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 27 (1971), 623-626
- MSC: Primary 13.90; Secondary 57.00
- DOI: https://doi.org/10.1090/S0002-9939-1971-0269642-2
- MathSciNet review: 0269642