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翻訳と辞書　辞書検索 [ 開発暫定版 ] スポンサード リンク Associated bundle ： ウィキペディア英語版 Associated bundle 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 $F\_1$ to $F\_2$, 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''α and ''U''β are given as a ''G''-valued function ''g''αβ on ''U''α∩''U''β. One may then construct a fibre bundle ''F''′ as a new fibre bundle having the same transition functions, but possibly a different fibre. ==An example== A simple case comes with the Möbius strip, for which $G$ is the cyclic group of order 2, $\backslash mathbb\_2$. We can take as $F$ any of: the real number line $\backslash mathbb$, the interval $(1)$, the real number line less the point 0, or the two-point set $\backslash$. The action of $G$ on these (the non-identity element acting as $x\backslash \; \backslash rightarrow\backslash \; -x$ in each case) is comparable, in an intuitive sense. We could say that more formally in terms of gluing two rectangles $(1)\; \backslash times\; I$ and $(1)\; \backslash times\; J$ together: what we really need is the data to identify $(1)$ to itself directly ''at one end'', and with the twist over ''at the other end''. This data can be written down as a patching function, with values in ''G''. The associated bundle construction is just the observation that this data does just as well for $\backslash$ as for $(1)$. 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「Associated bundle」の詳細全文を読む スポンサード リンク 翻訳と辞書 : 翻訳のためのインターネットリソース Copyright(C) kotoba.ne.jp 1997-2016. All Rights Reserved.