Hiroshima Mathematical Journal

Stable extendibility of some complex vector bundles over lens spaces and Schwarzenberger’s theorem

Yutaka Hemmi and Teiichi Kobayashi

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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.

Article information

Source
Hiroshima Math. J., Volume 46, Number 3 (2016), 333-341.

Dates
Received: 2 February 2016
Revised: 30 August 2016
First available in Project Euclid: 25 February 2017

Permanent link to this document
https://projecteuclid.org/euclid.hmj/1487991625

Digital Object Identifier
doi:10.32917/hmj/1487991625

Mathematical Reviews number (MathSciNet)
MR3614301

Zentralblatt MATH identifier
1367.55008

Subjects
Primary: 55R50: Stable classes of vector space bundles, $K$-theory [See also 19Lxx] {For algebraic $K$-theory, see 18F25, 19-XX}
Secondary: 55N15: $K$-theory [See also 19Lxx] {For algebraic $K$-theory, see 18F25, 19- XX}

Keywords
complex vector bundle extendible stably extendible K-theory lens space complex projective space

Citation

Hemmi, Yutaka; Kobayashi, Teiichi. Stable extendibility of some complex vector bundles over lens spaces and Schwarzenberger’s theorem. Hiroshima Math. J. 46 (2016), no. 3, 333--341. doi:10.32917/hmj/1487991625. https://projecteuclid.org/euclid.hmj/1487991625


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