翻訳と辞書 Words near each other ・ Eulepte vogli ・ Euleptes ・ Euleptorhamphus ・ Euleptus ・ Euler (crater) ・ Euler (disambiguation) ・ Euler (programming language) ・ Euler (software) ・ Euler (surname) ・ Euler angles ・ Euler Book Prize ・ Euler brick ・ Euler calculus ・ Euler characteristic ・ Euler circle ・ Euler class ・ Euler Committee of the Swiss Academy of Sciences ・ Euler D.I ・ Euler D.II ・ Euler diagram ・ Euler equations (fluid dynamics) ・ Euler filter ・ Euler force ・ Euler function ・ Euler Granda ・ Euler Hermes ・ Euler Hydro-triplane ・ Euler integral ・ Euler line ・ Euler method 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 Euler class ： ウィキペディア英語版 Euler class In mathematics, specifically in algebraic topology, the Euler class, named after Leonhard Euler, is a characteristic class of oriented, real vector bundles. Like other characteristic classes, it measures how "twisted" the vector bundle is. In the case of the tangent bundle of a smooth manifold, it generalizes the classical notion of Euler characteristic. Throughout this article ''E'' → ''X'' is an oriented, real vector bundle of rank ''r''. == Formal definition == The Euler class ''e''(''E'') is an element of the integral cohomology group :$H^r(X;\; \backslash mathbf),$ constructed as follows. An orientation of ''E'' amounts to a continuous choice of generator of the cohomology :$H^r(F,\; F\; \backslash setminus\; F\_0;\; \backslash mathbf)$ of each fiber ''F'' relative to the complement ''F''\''F''0 of its zero element ''F''0. From Thom isomorphism, this induces an orientation class :$u\; \backslash in\; H^r(E,\; E\; \backslash setminus\; E\_0;\; \backslash mathbf)$ in the cohomology of ''E'' relative to the complement ''E''\''E''0 of the zero section ''E''0. The inclusions :$(X,\; \backslash emptyset)\; \backslash hookrightarrow\; (E,\; \backslash emptyset)\; \backslash hookrightarrow\; (E,\; E\; \backslash setminus\; E\_0),$ where ''X'' includes into ''E'' as the zero section, induce maps :$H^r(E,\; E\; \backslash setminus\; E\_0;\; \backslash mathbf)\; \backslash to\; H^r(E;\; \backslash mathbf)\; \backslash to\; H^r(X;\; \backslash mathbf).$ The Euler class ''e''(''E'') is the image of ''u'' under the composition of these maps. 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「Euler class」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.