The purpose of this paper is to establish the formulas on the power of the normal bundle associated to an immersion of the real projective space $\RP^n$ in the Euclidean space $\R^{n+k}$, and apply them to the problem of extendibility and stable extendibility. Furthermore, we give an example of a $2$-dimensional $\R$-vector bundle over $\RP^2$ that is stably extendible to $\RP^3$ but is not extendible to $\RP^3$.
Publié le : 2007-03-14
Classification:
Vector bundle,
extendible,
stably extendible,
real projective space,
power of normal bundle,
tensor product,
$KO$-theory,
$K$-theory,
57R42,
55R50
@article{1176324097,
author = {Hemmi, Yutaka and Kobayashi, Teiichi and Lwin Oo, Min},
title = {The power of the normal bundle associated to an immersion of $\RP^n$, its complexification and extendibility},
journal = {Hiroshima Math. J.},
volume = {37},
number = {1},
year = {2007},
pages = { 101-109},
language = {en},
url = {http://dml.mathdoc.fr/item/1176324097}
}
Hemmi, Yutaka; Kobayashi, Teiichi; Lwin Oo, Min. The power of the normal bundle associated to an immersion of $\RP^n$, its complexification and extendibility. Hiroshima Math. J., Tome 37 (2007) no. 1, pp. 101-109. http://gdmltest.u-ga.fr/item/1176324097/