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Vector bundle

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  1. In mathematics, a vector bundle is a topological construction which makes precise the idea of a family of vector spaces parameterized by another space X (for example X could be a topological space, a manifold, or an algebraic variety)

    Source: Wikipedia Unhappy with this fact? more info
    created by user picturefactobot on December 10, 2008
  2. in this case there is a copy of V for each x in X and these copies fit together to form the vector bundle X×V over X. Such vector bundles are said to be trivial

    Source: Wikipedia Unhappy with this fact? more info
    created by user picturefactobot on December 10, 2008
  3. A more complicated (and prototypical) class of examples are the tangent bundles of smooth (or differentiable) manifolds: to every point of such a manifold we attach the tangent space to the manifold at that point

    Source: Wikipedia Unhappy with this fact? more info
    created by user picturefactobot on December 10, 2008
  4. Tangent bundles are not, in general, trivial bundles: for example, the tangent bundle of the (two dimensional) sphere is not trivial by the Hairy ball theorem

    Source: Wikipedia Unhappy with this fact? more info
    created by user picturefactobot on December 10, 2008
  5. are almost always required to be locally trivial, however, which means they are examples of fiber bundles

    Source: Wikipedia Unhappy with this fact? more info
    created by user picturefactobot on December 10, 2008
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