翻訳と辞書 Words near each other ・ Orientation ・ Orientation (computer vision) ・ Orientation (EP) ・ Orientation (geometry) ・ Orientation (graph theory) ・ Orientation (Heroes) ・ Orientation (Lost) ・ Orientation (mental) ・ Orientation (sign language) ・ Orientation (vector space) ・ Orientation and Mobility ・ Orientation camps in Hong Kong ・ Orientation character ・ Orientation column ・ Orientation entanglement ・ Orientation of a vector bundle ・ Orientation of churches ・ Orientation sensing ・ Orientation tensor ・ Orientational glass ・ Orientations ・ Orientations of Proteins in Membranes database ・ Orientative case ・ OrientDB ・ Oriente ・ Oriente (comarca) ・ Oriente (Ecuador) ・ Oriente cave rat ・ Oriente Petrolero ・ Oriente Petrolero in South America Dictionary Lists mini英和辞書 mini和英辞書 Webster 1913 Latin-English FOLDOC Wikipedia English ウィキペディア

翻訳と辞書　辞書検索 [ 開発暫定版 ] スポンサード リンク Orientation of a vector bundle ： ウィキペディア英語版 Orientation of a vector bundle In mathematics, an orientation of a real vector bundle is a generalization of an orientation of a vector space; thus, given a real vector bundle π: ''E'' →''B'', an orientation of ''E'' means: for each fiber ''E''''x'', there is an orientation of the vector space ''E''''x'' and one demands that each trivialization map (which is a bundle map) :$\backslash phi\_U\; :\; \backslash pi^(U)\; \backslash to\; U\; \backslash times\; \backslash mathbf^n$ is fiberwise orientation-preserving, where R''n'' is given the standard orientation. In more concise terms, this says that the structure group of the frame bundle of ''E'', which is the real general linear group ''GL''n(R), can be reduced to the subgroup consisting of those with positive determinant. A vector bundle together with an orientation is called an oriented bundle. Just as a real vector bundle is classified by the real infinite Grassmannian, oriented bundles are classified by the infinite Grassmannian of oriented real vector spaces. The basic invariant of an oriented bundle is the Euler class. The multiplication (that is, cup product) by the Euler class of an oriented bundle gives rise to a Gysin sequence. == Thom space == (詳細はThom space ''T''(''E'') such that ''u'' generates $\backslash tilde^$ *(T(E); \Lambda) as a free $H^$ *(E; \Lambda)-module globally and locally: i.e., :$H^$ *(E; \Lambda) \to \tilde^ *(T(E); \Lambda), x \mapsto x \cup u is an isomorphism (called the Thom isomorphism), where "tilde" means reduced cohomology, that restricts to each isomorphism :$H^$ *(\pi^(U); \Lambda) \to \tilde^ *(T(E|_U); \Lambda) induced by the trivialization $\backslash pi^(U)\; \backslash simeq\; U\; \backslash times\; \backslash mathbf^n$. One can show, with some work, that the usual notion of an orientation coincides with a Z-orientation. 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「Orientation of a vector 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.