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Vector bundle. The (infinitely extended) Möbius strip is a line bundle over the 1-sphere S1. Locally around every point in S1, it looks like U × R (where U is an open arc including the point), but the total bundle is different from S1 × R (which is a cylinder instead). In mathematics, a vector bundle is a topological construction that makes ...
Stable vector bundle. In mathematics, a stable vector bundle is a ( holomorphic or algebraic) vector bundle that is stable in the sense of geometric invariant theory. Any holomorphic vector bundle may be built from stable ones using Harder–Narasimhan filtration. Stable bundles were defined by David Mumford in Mumford (1963) and later built ...
One example of a principal bundle is the frame bundle. If for each two points b 1 and b 2 in the base, the corresponding fibers p −1 (b 1) and p −1 (b 2) are vector spaces of the same dimension, then the bundle is a vector bundle if the appropriate conditions of local triviality are satisfied. The tangent bundle is an example of a vector ...
C. Canonical bundle. Clifford bundle. Clifford module bundle. Coherent sheaf. Coherent sheaf cohomology. Complex vector bundle. Connection (vector bundle) Cotangent bundle.
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Important examples of vector bundles include the tangent bundle and cotangent bundle of a smooth manifold. From any vector bundle, one can construct the frame bundle of bases, which is a principal bundle (see below). Another special class of fiber bundles, called principal bundles, are bundles on whose fibers a free and transitive action by a ...
In the mathematical field of topology, a section (or cross section) [1] of a fiber bundle is a continuous right inverse of the projection function . In other words, if is a fiber bundle over a base space, : then a section of that fiber bundle is a continuous map , such that. for all . A section is an abstract characterization of what it means ...
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