翻訳と辞書 Words near each other ・ De re metallica ・ De Re Militari ・ De re publica ・ De rebus bellicis ・ De rebus Hispaniae ・ De Redin towers ・ De Regt ・ De Reiger, Nijetrijne ・ De remediis utriusque fortunae ・ De Rentmeester, Menaldum ・ De Renzie Brett ・ De rerum natura ・ De retour à la source ・ De revolutie! ・ De revolutionibus orbium coelestium ・ De Rham cohomology ・ De Rham curve ・ De Rham invariant ・ De Rham–Weil theorem ・ De Riancey ・ De Ribera ・ De Ridder ・ De Rietschoof ・ De Rietvink, Nijetrijne ・ De RigueurMortis ・ De Rijp ・ De Rips ・ De Rivaz engine ・ De River ・ De Robeck 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 De Rham cohomology ： ウィキペディア英語版 De Rham cohomology In mathematics, de Rham cohomology (after Georges de Rham) is a tool belonging both to algebraic topology and to differential topology, capable of expressing basic topological information about smooth manifolds in a form particularly adapted to computation and the concrete representation of cohomology classes. It is a cohomology theory based on the existence of differential forms with prescribed properties. ==Definition== The de Rham complex is the cochain complex of exterior differential forms on some smooth manifold , with the exterior derivative as the differential. :$0\; \backslash to\; \backslash Omega^0(M)\backslash \; \backslash stackrel\backslash \; \backslash Omega^1(M)\backslash \; \backslash stackrel\backslash \; \backslash Omega^2(M)\backslash \; \backslash stackrel\backslash \; \backslash Omega^3(M)\; \backslash to\; \backslash cdots$ where is the space of smooth functions on , is the space of -forms, and so forth. Forms which are the image of other forms under the exterior derivative, plus the constant function in are called exact and forms whose exterior derivative is are called closed (see closed and exact differential forms); the relationship then says that exact forms are closed. The converse, however, is not in general true; closed forms need not be exact. A simple but significant case is the -form of angle measure on the unit circle, written conventionally as (described at closed and exact differential forms). There is no actual function defined on the whole circle of which is the derivative; the increment of in going once round the circle in the positive direction means that we can't take a single-valued . We can, however, change the topology by removing just one point. The idea of de Rham cohomology is to classify the different types of closed forms on a manifold. One performs this classification by saying that two closed forms are cohomologous if they differ by an exact form, that is, if is exact. This classification induces an equivalence relation on the space of closed forms in . One then defines the -th de Rham cohomology group $H^\_\_^n.$ This follows from the fact that any smooth function on with zero derivative (i.e. locally constant) is constant on each of the connected components of . 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「De Rham cohomology」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.