Hiroshima Mathematical Journal

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

Yutaka Hemmi, Teiichi Kobayashi, and Min Lwin Oo

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Abstract

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 $\RP^3$.

Article information

Source
Hiroshima Math. J., Volume 37, Number 1 (2007), 101-109.

Dates
First available in Project Euclid: 11 April 2007

Permanent link to this document
https://projecteuclid.org/euclid.hmj/1176324097

Digital Object Identifier
doi:10.32917/hmj/1176324097

Mathematical Reviews number (MathSciNet)
MR2308526

Zentralblatt MATH identifier
1129.57034

Subjects
Primary: 57R42: Immersions
Secondary: 55R50: Stable classes of vector space bundles, $K$-theory [See also 19Lxx] {For algebraic $K$-theory, see 18F25, 19-XX}

Keywords
Vector bundle extendible stably extendible real projective space power of normal bundle tensor product $KO$-theory $K$-theory

Citation

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. 37 (2007), no. 1, 101--109. doi:10.32917/hmj/1176324097. https://projecteuclid.org/euclid.hmj/1176324097


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