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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 cap product ： ウィキペディア英語版 cap product In algebraic topology the cap product is a method of adjoining a chain of degree ''p'' with a cochain of degree ''q'', such that ''q'' ≤ ''p'', to form a composite chain of degree ''p'' − ''q''. It was introduced by Eduard Čech in 1936, and independently by Hassler Whitney in 1938. ==Definition== Let ''X'' be a topological space and ''R'' a coefficient ring. The cap product is a bilinear map on singular homology and cohomology :$\backslash frown\backslash ;:\; H\_p(X;R)\backslash times\; H^q(X;R)\; \backslash rightarrow\; H\_(X;R).$ defined by contracting a singular chain $\backslash sigma\; :\; \backslash Delta\backslash \; ^p\; \backslash rightarrow\backslash \; X$ with a singular cochain $\backslash psi\; \backslash in\; C^q(X;R),$ by the formula : :$\backslash sigma\; \backslash frown\; \backslash psi\; =\; \backslash psi(\backslash sigma|\_)\; \backslash sigma|\_.$ Here, the notation $\backslash sigma|\_$ indicates the restriction of the simplicial map $\backslash sigma$ to its face spanned by the vectors of the base, see Simplex. 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「cap product」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.