Stable extendibility of vector bundles over lens spaces mod 3 and the stable splitting problem

Let L n ( 3 ) denote the ( 2 n + 1 ) -dimensional standard lens space mod 3. In this paper, we study the conditions for a given real vector bundle over L n ( 3 ) to be stably extendible to L m ( 3 ) for every m ⩾ n , and establish the formula on the power ζ k = ζ ⊗ ⋯ ⊗ ζ ( k-fold) of a real vector b...

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Bibliographic Details
Published in:Topology and its applications 2009-09, Vol.156 (15), p.2485-2490
Main Authors: Hemmi, Yutaka, Kobayashi, Teiichi, Komatsu, Kazushi
Format: Article
Language:English
Subjects:
Extendibility
KO-theory
Lens space
Power of tangent bundle
Power of vector bundle
Stable extendibility
Tangent bundle
Vector bundle
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Summary:Let L n ( 3 ) denote the ( 2 n + 1 ) -dimensional standard lens space mod 3. In this paper, we study the conditions for a given real vector bundle over L n ( 3 ) to be stably extendible to L m ( 3 ) for every m ⩾ n , and establish the formula on the power ζ k = ζ ⊗ ⋯ ⊗ ζ ( k-fold) of a real vector bundle ζ over L n ( 3 ) . Moreover, we answer the stable splitting problem for real vector bundles over L n ( 3 ) by means of arithmetic conditions.
ISSN:0166-8641
1879-3207
DOI:10.1016/j.topol.2009.07.003