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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 is a CW-complex with n-skeleton , the cellular-homology modules are defined as the homology groups of the cellular chain complex : where is taken to be the empty set. The group : is free abelian, with generators that can be identified with the -cells of . Let be an -cell of , and let be the attaching map. Then consider the composition : where the first map identifies with via the characteristic map of , the object is an -cell of ''X'', the third map is the quotient map that collapses to a point (thus wrapping into a sphere ), and the last map identifies with via the characteristic map of . The boundary map : is then given by the formula : where is the degree of and the sum is taken over all -cells of , considered as generators 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「Cellular homology」の詳細全文を読む スポンサード リンク
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