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subbundle (Definition)

Given a vector bundle $\pi \!:\! \mathcal E \rightarrow M$ a subbundle $\mathcal E^\prime$ is a subset of the total space, $\mathcal E^\prime \subset \mathcal E$ so that $$ \pi\vert_{\mathcal E^\prime}\!:\! \mathcal E^\prime \rightarrow M$$ is a vector bundle, and for each point $p\in M$ the fibre at $p$ $${\pi\vert_{\mathcal E^{\prime}}}^{-1}(p) = \mathcal E^\prime_p$$ is a vector subspace of $\mathcal E_p = \pi^{-1}(p)$



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Other names:  sub-bundle, vector sub-bundle, vector subbundle, sub-vector bundle, sub vector bundle
Also defines:  subbundle
Keywords:  subbundle, vector bundle, sub-bundle, sub-vector bundle
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Cross-references: vector subspace, fibre, point, subset, vector bundle
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This is version 1 of subbundle, born on 2007-03-18.
Object id is 9094, canonical name is Subbundle.
Accessed 2996 times total.

Classification:
AMS MSC14F05 (Algebraic geometry :: homology theory :: Vector bundles, sheaves, related constructions)
 55R25 (Algebraic topology :: Fiber spaces and bundles :: Sphere bundles and vector bundles)

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