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.
Citation
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