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November 2016 Stable extendibility of some complex vector bundles over lens spaces and Schwarzenberger’s theorem
Yutaka Hemmi, Teiichi Kobayashi
Hiroshima Math. J. 46(3): 333-341 (November 2016). DOI: 10.32917/hmj/1487991625

Abstract

We obtain conditions for stable extendibility of some complex vector bundles over the $(2n + 1)$-dimensional standard lens space $L^n(p) \operatorname{mod} p$, where $p$ is a prime. Furthermore, we study stable extendibility of the bundle $\pi^*_n (\tau(\mathbf{C}P^n))$ induced by the natural projection $\pi_n : L^n(p)\to \mathbf{C}P^n$ from the complex tangent bundle $\tau(\mathbf{C}P^n)$ of the complex projective $n$-space $\mathbf{C}P^n$. As an application, we have a result on stable extendibility of $\tau(\mathbf{C}P^n)$ which gives another proof of Schwarzenberger’s theorem.

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Yutaka Hemmi. Teiichi Kobayashi. "Stable extendibility of some complex vector bundles over lens spaces and Schwarzenberger’s theorem." Hiroshima Math. J. 46 (3) 333 - 341, November 2016. https://doi.org/10.32917/hmj/1487991625

Information

Received: 2 February 2016; Revised: 30 August 2016; Published: November 2016
First available in Project Euclid: 25 February 2017

zbMATH: 1367.55008
MathSciNet: MR3614301
Digital Object Identifier: 10.32917/hmj/1487991625

Subjects:
Primary: 55R50
Secondary: 55N15

Rights: Copyright © 2016 Hiroshima University, Mathematics Program

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Vol.46 • No. 3 • November 2016
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