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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 Homotopy excision theorem ： ウィキペディア英語版 Homotopy excision theorem In algebraic topology, the homotopy excision theorem offers a substitute for the absence of excision in homotopy theory. More precisely, let $(X;\; A,\; B)$ be an excisive triad with $C\; =\; A\; \backslash cap\; B$ nonempty, and suppose the pair $(A,\; C)$ is ($m-1$)-connected, $m\; \backslash ge\; 2$, and the pair $(B,\; C)$ is ($n-1$)-connected, $n\; \backslash ge\; 1$. Then the map induced by the inclusion $i:\; (A,\; C)\; \backslash to\; (X,\; B)$ :$i\_$ *: \pi_q(A, C) \to \pi_q(X, B) is bijective for and is surjective for $q\; =\; m+n-2$. A nice geometric proof is given in the book by tom Dieck.〔T. tom Dieck, ''Algebraic Topology'', EMS Textbooks in Mathematics, (2008).〕 This result should also be seen as a consequence of the Blakers–Massey theorem, the most general form of which, dealing with the non-simply-connected case.〔R. Brown and J.-L. Loday, ''Homotopical excision and Hurewicz theorems for ''n''-cubes of spaces'', Proc. London Math. Soc., (3) 54 (1987) 176-192.〕 The most important consequence is the Freudenthal suspension theorem. == References == 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「Homotopy excision theorem」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.