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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 Eilenberg–Moore spectral sequence ： ウィキペディア英語版 Eilenberg–Moore spectral sequence In mathematics, in the field of algebraic topology, the Eilenberg–Moore spectral sequence addresses the calculation of the homology groups of a pullback over a fibration. The spectral sequence formulates the calculation from knowledge of the homology of the remaining spaces. Samuel Eilenberg and John C. Moore's original paper addresses this for singular homology. ==Motivation== Let $k$ be a field and :$H\_\backslash ast(-)=H\_\backslash ast(-,k),\; H^\backslash ast(-)=H^\backslash ast(-,k)$ denote singular homology and singular cohomology with coefficients in ''k'', respectively. Consider the following pullback ''Ef'' of a continuous map ''p'': : A frequent question is how the homology of the fiber product ''Ef'', relates to the ones of ''B'', ''X'' and ''E''. For example, if ''B'' is a point, then the pullback is just the usual product ''E'' × ''X''. In this case the Künneth formula says :''H''∗(''Ef'') = ''H''∗(''X''×''E'') ≅ ''H''∗(''X'') ⊗k ''H''∗(''E''). However this relation is not true in more general situations. The Eilenberg−Moore spectral sequence is a device which allows the computation of the (co)homology of the fiber product in certain situations. 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「Eilenberg–Moore 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.