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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 Clutching construction ： ウィキペディア英語版 Clutching construction In topology, a branch of mathematics, the clutching construction is a way of constructing fiber bundles, particularly vector bundles on spheres. ==Definition== Consider the sphere $S^n$ as the union of the upper and lower hemispheres $D^n\_+$ and $D^n\_-$ along their intersection, the equator, an $S^$. Given trivialized fiber bundles with fiber $F$ and structure group $G$ over the two disks, then given a map $f\backslash colon\; S^\; \backslash to\; G$ (called the ''clutching map''), glue the two trivial bundles together via ''f''. Formally, it is the coequalizer of the inclusions $S^\; \backslash times\; F\; \backslash to\; D^n\_+\; \backslash times\; F\; \backslash coprod\; D^n\_-\; \backslash times\; F$ via $(x,v)\; \backslash mapsto\; (x,v)\; \backslash in\; D^n\_+\; \backslash times\; F$ and $(x,v)\; \backslash mapsto\; (x,f(x)(v))\; \backslash in\; D^n\_-\; \backslash times\; F$: glue the two bundles together on the boundary, with a twist. Thus we have a map $\backslash pi\_\; G\; \backslash to\; \backslash text\_F(S^n)$: clutching information on the equator yields a fiber bundle on the total space. In the case of vector bundles, this yields $\backslash pi\_\; O(k)\; \backslash to\; \backslash text\_k(S^n)$, and indeed this map is an isomorphism (under connect sum of spheres on the right). 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「Clutching construction」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.