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In mathematics, a microbundle is a generalization of the concept of vector bundle, introduced by the American mathematician John Milnor in 1964. It allows the creation of bundle-like objects in situations where they would not ordinarily be thought to exist. For example, the tangent bundle is defined for a smooth manifold but not a topological manifold. Use of microbundles allows the definition of a ''topological'' tangent bundle. ==Definition== The precise definition of a microbundle follows. Let ''B'' be a topological space. Then a ''n''-microbundle consists of a triple (E, i, p) where ''E'' is a topological space (the "total space"), ''i'' is a map from ''B'' to ''E'' (the "zero section"), and ''p'' is a map from ''E'' to ''B'' ("the projection map"). Furthermore there are two conditions: #the composition of ''i'' followed by ''p'' must be the identity; #for every ''b'' in ''B'', there must be a neighborhood ''V''''b'' in ''E'' such that ''p'' restricted to ''V''''b'' looks like a projection ''U''B × R''n'' → ''U''''b''. Note that the first condition suggests ''i'' is the zero section of a vector bundle, while the second is like the local triviality condition on a bundle. An important distinction here is that "local triviality" for microbundles only holds near a neighborhood of the zero section. ''E'' could look very wild away from that neighborhood. Also, the maps gluing together locally trivial patches of the microbundle may only overlap the fibers. 抄文引用元・出典: フリー百科事典『 ウィキペディア（Wikipedia）』 ■ウィキペディアで「Microbundle」の詳細全文を読む スポンサード リンク
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