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Vector bundle - Wikipedia, the free encyclopedia |
 | | In mathematics, a vector bundle is a geometrical construct where to every point of a topological space (or manifold, or algebraic variety) we attach a vector space in a compatible way, so that all those vector spaces, "glued together", form another topological space (or manifold or variety). |
| | A typical example is the tangent bundle of a differentiable manifold: to every point of the manifold we attach the tangent space of the manifold at that point. |
| | Smooth vector bundles are defined by requiring that E and X be smooth manifolds, π : E → X be a smooth map, and the local trivialization maps φ be diffeomorphisms. |
| en.wikipedia.org /wiki/Vector_bundle (1137 words) |
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