The purpose of this paper is to study the stable extendibility of the tangent bundle $\tau_n(p)$ of the $(2n+1)$-\hspace dimensional standard lens space $\mL^n(p)$ for odd prime $p$. We investigate the value of integer $m$ for which $\tau_n(p)$ is stably extendible to $\mL^m(p)$ but not stably extendible to $\mL^{m+1}(p)$, and in particular we completely determine $m$ for $p=5$ or $7$. A stable splitting of $\tau_n(p)$ and the stable extendibility of a Whitney sum of $\tau_n(p)$ are also discussed.
@article{1171377077,
author = {Imaoka, Mitsunori and Yamasaki, Hironori},
title = {Stable extendibility of the tangent bundles over lens spaces},
journal = {Hiroshima Math. J.},
volume = {36},
number = {1},
year = {2006},
pages = { 339-351},
language = {en},
url = {http://dml.mathdoc.fr/item/1171377077}
}
Imaoka, Mitsunori; Yamasaki, Hironori. Stable extendibility of the tangent bundles over lens spaces. Hiroshima Math. J., Tome 36 (2006) no. 1, pp. 339-351. http://gdmltest.u-ga.fr/item/1171377077/