Open Access
March 2007 A stability theorem for the index of sphere bundles
Ryuichi Tanaka
Bull. Belg. Math. Soc. Simon Stevin 14(1): 177-182 (March 2007). DOI: 10.36045/bbms/1172852252

Abstract

We prove that the index of every $m$-dimensional vector bundle over $B$ is equal to $m$ if $m \geq 2 dim{B}$. We also determine the smallest integer $k$ for which every $m$-dimensional vector bundle with $m\geq k$ is I-stable in the cases $B=FP^n$ and $B=S^n$.

Citation

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Ryuichi Tanaka. "A stability theorem for the index of sphere bundles." Bull. Belg. Math. Soc. Simon Stevin 14 (1) 177 - 182, March 2007. https://doi.org/10.36045/bbms/1172852252

Information

Published: March 2007
First available in Project Euclid: 2 March 2007

zbMATH: 1130.55007
MathSciNet: MR2327334
Digital Object Identifier: 10.36045/bbms/1172852252

Subjects:
Primary: 55P91
Secondary: 55R25

Keywords: $\mathbb Z/2$ -map , Index , radial solutions , Sphere bundle

Rights: Copyright © 2007 The Belgian Mathematical Society

Vol.14 • No. 1 • March 2007
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