The power of the normal bundle associated to an immersion of $\RP^n$, its complexification and extendibility

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-dime...

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Bibliographic Details
Published in:Hiroshima mathematical journal 2007-03, Vol.37 (1), p.101-109
Main Authors: Hemmi, Yutaka, Kobayashi, Teiichi, Lwin Oo, Min
Format: Article
Language:English
Subjects:
55R50
57R42
extendible
K-theory
KO-theory
power of normal bundle
real projective space
stably extendible
tensor product
Vector bundle
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Summary: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.
ISSN:0018-2079
DOI:10.32917/hmj/1176324097