Associated Bundle

In mathematics, the theory of fiber bundles with a structure group (a topological group) allows an operation of creating an associated bundle, in which the typical fiber of a bundle changes from to, which are both topological spaces with a group action of . For a fibre bundle F with structure group G, the transition functions of the fibre (i.e., the cocycle) in an overlap of two coordinate systems Uα and Uβ are given as a G-valued function gαβ on UαUβ. One may then construct a fibre bundle F′ as a new fibre bundle having the same transition functions, but possibly a different fibre.

Read more about Associated Bundle:  An Example, Construction, Reduction of The Structure Group

Famous quotes containing the word bundle:

    We styled ourselves the Knights of the Umbrella and the Bundle; for, wherever we went ... the umbrella and the bundle went with us; for we wished to be ready to digress at any moment. We made it our home nowhere in particular, but everywhere where our umbrella and bundle were.
    Henry David Thoreau (1817–1862)