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March 2018 Stable extendibility and extendibility of vector bundles over lens spaces
Mitsunori Imaoka, Teiichi Kobayashi
Hiroshima Math. J. 48(1): 57-66 (March 2018). DOI: 10.32917/hmj/1520478023


Firstly, we obtain conditions for stable extendibility and extendibility of complex vector bundles over the $(2n+1)$-dimensional standard lens space $L^n(p)$ mod $p$, where $p$ is a prime. Secondly, we prove that the complexification $c(\tau_n(p))$ of the tangent bundle $\tau_n(p) (=\tau(L^n(p)))$ of $L^n(p)$ is extendible to $L^{2n+1}(p)$ if $p$ is a prime, and is not stably extendible to $L^{2n+2}(p)$ if $p$ is an odd prime and $n \ge 2p-2$. Thirdly, we show, for some odd prime $p$ and positive integers $n$ and $m$ with $m > n$, that $\tau(L^n(p))$ is stably extendible to $L^m(p)$ but is not extendible to $L^m(p)$.


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Mitsunori Imaoka. Teiichi Kobayashi. "Stable extendibility and extendibility of vector bundles over lens spaces." Hiroshima Math. J. 48 (1) 57 - 66, March 2018.


Received: 14 September 2016; Revised: 16 June 2017; Published: March 2018
First available in Project Euclid: 8 March 2018

zbMATH: 06329508
MathSciNet: MR3772000
Digital Object Identifier: 10.32917/hmj/1520478023

Primary: 55R50
Secondary: 57R25

Rights: Copyright © 2018 Hiroshima University, Mathematics Program


Vol.48 • No. 1 • March 2018
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