翻訳と辞書 Words near each other ・ Spectral mutability ・ Spectral network ・ Spectral noise logging ・ Spectral phase interferometry for direct electric-field reconstruction ・ Spectral power distribution ・ Spectral printing ・ Spectral purity ・ Spectral pygmy chameleon ・ Spectral radius ・ Spectral regrowth ・ Spectral rendering ・ Spectral resolution ・ Spectral risk measure ・ Spectral Sciences Incorporated ・ Spectral sensitivity ・ Spectral sequence ・ Spectral set ・ Spectral shape analysis ・ Spectral signal-to-noise ratio ・ Spectral signature ・ Spectral slope ・ Spectral Sound ・ Spectral space ・ Spectral splatter ・ Spectral tarsier ・ Spectral test ・ Spectral theorem ・ Spectral theory ・ Spectral theory of compact operators ・ Spectral theory of ordinary differential equations 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 Spectral sequence ： ウィキペディア英語版 Spectral sequence In homological algebra and algebraic topology, a spectral sequence is a means of computing homology groups by taking successive approximations. Spectral sequences are a generalization of exact sequences, and since their introduction by , they have become important computational tools, particularly in algebraic topology, algebraic geometry and homological algebra. == Discovery and motivation == Motivated by problems in algebraic topology, Jean Leray introduced the notion of a sheaf and found himself faced with the problem of computing sheaf cohomology. To compute sheaf cohomology, Leray introduced a computational technique now known as the Leray spectral sequence. This gave a relation between cohomology groups of a sheaf and cohomology groups of the pushforward of the sheaf. The relation involved an infinite process. Leray found that the cohomology groups of the pushforward formed a natural chain complex, so that he could take the cohomology of the cohomology. This was still not the cohomology of the original sheaf, but it was one step closer in a sense. The cohomology of the cohomology again formed a chain complex, and its cohomology formed a chain complex, and so on. The limit of this infinite process was essentially the same as the cohomology groups of the original sheaf. It was soon realized that Leray's computational technique was an example of a more general phenomenon. Spectral sequences were found in diverse situations, and they gave intricate relationships among homology and cohomology groups coming from geometric situations such as fibrations and from algebraic situations involving derived functors. While their theoretical importance has decreased since the introduction of derived categories, they are still the most effective computational tool available. This is true even when many of the terms of the spectral sequence are incalculable. Unfortunately, because of the large amount of information carried in spectral sequences, they are difficult to grasp. This information is usually contained in a rank three lattice of abelian groups or modules. The easiest cases to deal with are those in which the spectral sequence eventually collapses, meaning that going out further in the sequence produces no new information. Even when this does not happen, it is often possible to get useful information from a spectral sequence by various tricks. 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「Spectral sequence」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.