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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 Relative homology ： ウィキペディア英語版 Relative homology In algebraic topology, a branch of mathematics, the (singular) homology of a topological space relative to a subspace is a construction in singular homology, for pairs of spaces. The relative homology is useful and important in several ways. Intuitively, it helps determine what part of an absolute homology group comes from which subspace. == Definition == Given a subspace $A\backslash subset\; X$, one may form the short exact sequence :$0\backslash to\; C\_\backslash bullet(A)\; \backslash to\; C\_\backslash bullet(X)\backslash to$ C_\bullet(X) /C_\bullet(A) \to 0 where $C\_\backslash bullet(X)$ denotes the singular chains on the space ''X''. The boundary map on $C\_\backslash bullet(X)$ leaves $C\_\backslash bullet(A)$ invariant and therefore descends to a boundary map on the quotient. The corresponding homology is called relative homology: :$H\_n(X,A)\; =\; H\_n\; (C\_\backslash bullet(X)\; /C\_\backslash bullet(A)).$ One says that relative homology is given by the relative cycles, chains whose boundaries are chains on ''A'', modulo the relative boundaries (chains that are homologous to a chain on ''A'', i.e. chains that would be boundaries, modulo ''A'' again). 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「Relative homology」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.