Hiroshima Mathematical Journal

Stable extendibility and extendibility of vector bundles over lens spaces

Mitsunori Imaoka and Teiichi Kobayashi

Full-text: Open access

Abstract

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 $L^m(p)$.

Article information

Source
Hiroshima Math. J., Volume 48, Number 1 (2018), 57-66.

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

Permanent link to this document
https://projecteuclid.org/euclid.hmj/1520478023

Digital Object Identifier
doi:10.32917/hmj/1520478023

Mathematical Reviews number (MathSciNet)
MR3772000

Zentralblatt MATH identifier
06329508

Subjects
Primary: 55R50: Stable classes of vector space bundles, $K$-theory [See also 19Lxx] {For algebraic $K$-theory, see 18F25, 19-XX}
Secondary: 57R25: Vector fields, frame fields

Keywords
vector bundle tangent bundle lens space extendible stably extendible K-theory

Citation

Imaoka, Mitsunori; Kobayashi, Teiichi. Stable extendibility and extendibility of vector bundles over lens spaces. Hiroshima Math. J. 48 (2018), no. 1, 57--66. doi:10.32917/hmj/1520478023. https://projecteuclid.org/euclid.hmj/1520478023


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