Stable unextendibility of vector bundles over the quaternionic projective spaces

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概要

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• We study the stable unextendibility of vector bundles over the quaternionic projective space HP^n by making use of combinatorial properties of the Stiefel-Whitney classes and the Pontrjagin classes. First, we show that the tangent bundle of HP^n is not stably extendible to HP^<n+1> for n ≥ 2, and also induce such a result for the normal bundle associated to an immersion of HP^n into R^<4n+k>. Secondly, we show a sufficient condition for a quaternionic r-dimensional vector bundle over HP^n not to be stably extendible to HP^<n+l> for r ≤ n and l > 0, which is also a necessary condition when r = n and l = 1.

• 広島大学の論文

著者

• Imaoka Mitsunori

  Department Of Mathematics Education Graduate Course Of Education Hiroshima University

• Imaoka Mitsunori

  Department Of Mathematcs Faculty Of Education Hiroshima University

関連論文

• On the stable Hurewicz image of some stunted projective spaces,3
• Extendiblity of negative vector bundles over the complex projective spaces
• On the Stable Hurewicz Image of Some Stunted Projective Spaces, II : Dedicated to Professor N. Shimada on his 60th birthday
• On the Adams Filtration of a Generator of the Free Part of $\pi\sp s\sb *(Q\sb n)$ / Dedicated to Professor Shoro Araki on his sixtieth birthday
• Symmetricity of the Whitehead element
• On the Stable Hurewicz Image of Some Stunted Projective Spaces,I : Dedicated to Professor N. Shimada on his 60th birthday
• Stable unextendibility of vector bundles over the quaternionic projective spaces
• Stable extendibility of the tangent bundles over the lens spaces
• Transfer maps of sphere bundles

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