翻訳と辞書 Words near each other ・ Pusher (boat) ・ Pusher (film series) ・ Pusher (railway station attendant) ・ Pusher (tennis) ・ Pusher (The X-Files) ・ Pusher 3 ・ Pusher centrifuge ・ Pusher configuration ・ Pusher II ・ Pusher Love Girl ・ Pusher trailer ・ Pusherman ・ Pusheta Township, Auglaize County, Ohio ・ Pushforward ・ Pushforward (differential) ・ Pushforward (homology) ・ Pushforward measure ・ Pushihe Pumped Storage Power Station ・ Pushim ・ Pushin Forward Back ・ Pushin' Against a Stone ・ Pushin' Me Away ・ Pushin' On ・ Pushin' Too Hard ・ Pushin' Up Daisies ・ Pushin' Weight ・ Pushing Buttons ・ Pushing Daisies ・ Pushing hands ・ Pushing Hands (film) Dictionary Lists mini英和辞書 mini和英辞書 Webster 1913 Latin-English FOLDOC Wikipedia English ウィキペディア

翻訳と辞書　辞書検索 [ 開発暫定版 ] スポンサード リンク Pushforward (homology) ： ウィキペディア英語版 Pushforward (homology) In algebraic topology, the pushforward of a continuous function $f$ : $X\; \backslash rightarrow\; Y$ between two topological spaces is a homomorphism $f\_:H\_n\backslash left(X\backslash right)\; \backslash rightarrow\; H\_n\backslash left(Y\backslash right)$ between the homology groups for $n\; \backslash geq\; 0$. Homology is a functor which converts a topological space $X$ into a sequence of homology groups $H\_\backslash left(X\backslash right)$. (Often, the collection of all such groups is referred to using the notation $H\_\backslash left(X\backslash right)$; this collection has the structure of a graded ring.) In any category, a functor must induce a corresponding morphism. The pushforward is the morphism corresponding to the homology functor. == Definition for singular and simplicial homology == We build the pushforward homomorphism as follows (for singular or simplicial homology): First we have an induced homomorphism between the singular or simplicial chain complex $C\_n\backslash left(X\backslash right)$ and $C\_n\backslash left(Y\backslash right)$ defined by composing each singular n-simplex $\backslash sigma\_X$ : $\backslash Delta^n\backslash rightarrow\; X$ with $f$ to obtain a singular n-simplex of $Y$, $f\_\backslash left(\backslash sigma\_X\backslash right)\; =\; f\backslash sigma\_X$ : $\backslash Delta^n\backslash rightarrow\; Y$. Then we extend $f\_$ linearly via $f\_\backslash left(\backslash sum\_tn\_t\backslash sigma\_t\backslash right)\; =\; \backslash sum\_tn\_tf\_\backslash left(\backslash sigma\_t\backslash right)$. The maps $f\_$ : $C\_n\backslash left(X\backslash right)\backslash rightarrow\; C\_n\backslash left(Y\backslash right)$ satisfy $f\_\backslash partial\; =\; \backslash partial\; f\_$ where $\backslash partial$ is the boundary operator between chain groups, so $\backslash partial\; f\_$ defines a chain map. We have that $f\_$ takes cycles to cycles, since $\backslash partial\; \backslash alpha\; =\; 0$ implies $\backslash partial\; f\_\backslash left(\; \backslash alpha\; \backslash right)\; =\; f\_\backslash left(\backslash partial\; \backslash alpha\; \backslash right)\; =\; 0$. Also $f\_$ takes boundaries to boundaries since $f\_\backslash left(\backslash partial\; \backslash beta\; \backslash right)\; =\; \backslash partial\; f\_\backslash left(\backslash beta\; \backslash right)$. Hence $f\_$ induces a homomorphism between the homology groups $f\_\; :\; H\_n\backslash left(X\backslash right)\; \backslash rightarrow\; H\_n\backslash left(Y\backslash right)$ for $n\backslash geq0$. 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「Pushforward (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.