Extendibility, stable extendibility and span of some vector bundles over lens spaces mod 3

概要

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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 [5] and [6], 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.
広島大学の論文
2007-03-00