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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 Toda–Smith complex ： ウィキペディア英語版 Toda–Smith complex In mathematics, Toda–Smith complexes are spectra characterized by having a particularly simple homology, and are used in stable homotopy theory. Toda–Smith complexes provided examples of periodic maps. Thus, they led to the construction of the nilpotent and periodicity theorems,〔https://books.google.com/books?id=xoM5DxQZihQC&pg=PA341&lpg=PA341&dq=Larry+Smith+algebraic+topology&source=bl&ots=pyH8hPMnye&sig=dVMAcZzrlqoTuKj010LhMe8dRIA&hl=en&sa=X&ved=0CDwQ6AEwBGoVChMI7af67tv3xgIVBzKICh0sbQWR#v=onepage&q=Larry%20Smith%20algebraic%20topology&f=false〕 which provided the first organization of the stable homotopy groups of spheres into families of maps localized at a prime. == Mathematical context == The story begins with the degree $p$ map on $S^1$ (as a circle in the complex plane): : $S^1\; \backslash to\; S^1\; \backslash ,$ : $z\; \backslash mapsto\; z^p\; \backslash ,$ The degree $p$ map is well defined for $S^k$ in general, where $k\; \backslash in\; \backslash mathbb$. If we apply the infinite suspension functor to this map, $\backslash Sigma^\backslash infty\; S^1\; \backslash to\; \backslash Sigma^\backslash infty\; S^1\; =:\; \backslash mathbb^1\; \backslash to\; \backslash mathbb^1$ and we take the cofiber of the resulting map: : $S\; \backslash xrightarrow\; S\; \backslash to\; S/p$ We find that $S/p$ has the remarkable property of coming from a Moore space (i.e., a designer (co)homology space: $H^n(X)\; \backslash simeq\; Z/p$, and $\backslash tilde^$ *(X) is trivial for all $$ * \neq n). It is also of note that the periodic maps, $\backslash alpha\_t$, $\backslash beta\_t$, and $\backslash gamma\_t$, come from degree maps between the Toda–Smith complexes, $V(0)\_k$, $V(1)\_k$, and $V\_2(k)$ respectively. 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「Toda–Smith complex」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.