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March 2007 Extendibility, stable extendibility and span of some vector bundles over lens spaces mod 3
Teiichi Kobayashi, Kazushi Komatsu
Hiroshima Math. J. 37(1): 45-60 (March 2007). DOI: 10.32917/hmj/1176324094

Abstract

Let $L^{n}(3)$ be the $(2n+1)$-dimensional standard lens space mod 3 and let $\nu$ denote the normal bundle associated to an immersion of $L^{n}(3)$ in the Euclidean $(4n+3)$-space. In this paper we obtain a theorem on stable unextendibility of $R$-vector bundles over $L^{n}(3)$ improving some results in Extendibility and stable extendibility of vector bundles over lens spaces and Stable extendibility of normal bundles associated to immersions of real projective spaces and lens spaces, and study relations between stable extendibility and span of vector bundles over $L^{n}(3)$. Furtheremore, we prove that $c\nu$ is extendible to $L^{m}(3)$ for every $m > n$ if and only if $0 \leq n \leq 5$, and prove that $c(\nu \otimes \nu)$ is extendible to $L^{m}(3)$ for every $m > n$ if and only if $0 \leq n \leq 13$ or $n = 15$, where $c$ stands for the complexification and $\otimes$ denotes the tensor product.

Citation

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Teiichi Kobayashi. Kazushi Komatsu. "Extendibility, stable extendibility and span of some vector bundles over lens spaces mod 3." Hiroshima Math. J. 37 (1) 45 - 60, March 2007. https://doi.org/10.32917/hmj/1176324094

Information

Published: March 2007
First available in Project Euclid: 11 April 2007

zbMATH: 1141.55010
MathSciNet: MR2308523
Digital Object Identifier: 10.32917/hmj/1176324094

Subjects:
Primary: 55R50
Secondary: 57R42

Rights: Copyright © 2007 Hiroshima University, Mathematics Program

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Vol.37 • No. 1 • March 2007
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