Extendible and stably extendible vector bundles over real projective spaces

被引:3
作者
Kobayashi, T [1 ]
Yoshida, T [1 ]
机构
[1] Hiroshima Univ, Fac Integrated Arts & Sci, Dept Math, Higashihiroshima 7398521, Japan
关键词
vector bundle; extendible; stably extendible; tangent bundle; span; immersion; normal bundle; K-theory; KO-theory; real projective space;
D O I
10.2969/jmsj/1191418763
中图分类号
O1 [数学];
学科分类号
0701 ; 070101 ;
摘要
The purpose of this paper is to study extendibility and stable extendibility of vector bundles over real projective spaces. We determine a necessary and sufficient condition that a vector bundle zeta over the real projective n-space RPn is extendible (or stably extendible) to RPm for every m > n in the case where zeta is the complexification of the tangent bundle of RPn and in the case where zeta is the normal bundle associated to an immersion of RPn in the Euclidean (n + k)-space Rn+k or its complexification, and give examples of the normal bundle which is extendible to RPN but is not stably extendible to RPN+1.
引用
收藏
页码:1053 / 1059
页数:7
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