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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 cellular homology ： ウィキペディア英語版 cellular homology In mathematics, cellular homology in algebraic topology is a homology theory for the category of CW-complexes. It agrees with singular homology, and can provide an effective means of computing homology modules. == Definition == If $X$ is a CW-complex with n-skeleton $X\_$, the cellular-homology modules are defined as the homology groups of the cellular chain complex :$$ \cdots \to ,X_) \to ,X_) \to ,X_) \to \cdots, where $X\_$ is taken to be the empty set. The group :$$ ,X_) is free abelian, with generators that can be identified with the $n$-cells of $X$. Let $e\_^$ be an $n$-cell of $X$, and let $\backslash chi\_^:\; \backslash partial\; e\_^\; \backslash cong\; \backslash mathbb^\; \backslash to\; X\_$ be the attaching map. Then consider the composition :$$ \chi_^: \mathbb^ \, \stackrel \, \partial e_^ \, \stackrel} \, X_ \, \stackrel \, X_ / \left( X_ \setminus e_^ \right) \, \stackrel \, \mathbb^, where the first map identifies $\backslash mathbb^$ with $\backslash partial\; e\_^$ via the characteristic map $\backslash Phi\_^$ of $e\_^$, the object $e\_^$ is an $(n\; -\; 1)$-cell of ''X'', the third map $q$ is the quotient map that collapses $X\_\; \backslash setminus\; e\_^$ to a point (thus wrapping $e\_^$ into a sphere $\backslash mathbb^$), and the last map identifies $X\_\; /\; \backslash left(\; X\_\; \backslash setminus\; e\_^\; \backslash right)$ with $\backslash mathbb^$ via the characteristic map $\backslash Phi\_^$ of $e\_^$. The boundary map :$$ d_: ,X_) \to ,X_) is then given by the formula :$$ ^) = \sum_ \deg \left( \chi_^ \right) e_^, where $\backslash deg\; \backslash left(\; \backslash chi\_^\; \backslash right)$ is the degree of $\backslash chi\_^$ and the sum is taken over all $(n\; -\; 1)$-cells of $X$, considered as generators of $,X\_)$. 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「cellular 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.