Please note that the content of this book primarily consists of articles available from Wikipedia or other free sources online. In mathematics, the theory of fiber bundles with a structure group G (a topological group) allows an operation of creating an associated bundle, in which the typical fiber of a bundle changes from F1 to F2, which are both topological spaces with a group action of G. 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 U and U are given as a G-valued function g on U U . One may then construct a fibre bundle F as a new fibre bundle having the same transition functions, but possibly a different fibre.

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