The stable geometric dimension of vector bundles over real projective spaces

Authors:
Donald M. Davis, Sam Gitler and Mark Mahowald

Journal:
Trans. Amer. Math. Soc. **268** (1981), 39-61

MSC:
Primary 55N15; Secondary 55R25

DOI:
https://doi.org/10.1090/S0002-9947-1981-0628445-8

Correction:
Trans. Amer. Math. Soc. **280** (1983), 841-843.

MathSciNet review:
628445

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Abstract | References | Similar Articles | Additional Information

Abstract: An elementary argument shows that the geometric dimension of any vector bundle of order over depends only on and the residue of for sufficiently large. In this paper we calculate this geometric dimension, which is approximately . The nonlifting results are easily obtained using the spectrum . The lifting results require -resolutions. Half of the paper is devoted to proving Mahowald's theorem that beginning with the second stage -resolutions act almost like -resolutions.

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Additional Information

DOI:
https://doi.org/10.1090/S0002-9947-1981-0628445-8

Keywords:
Geometric dimension of vector bundles,
real projective space,
obstruction theory,
-resolutions

Article copyright:
© Copyright 1981
American Mathematical Society