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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 EHP spectral sequence ： ウィキペディア英語版 EHP spectral sequence In mathematics, the EHP spectral sequence is a spectral sequence used for inductively calculating the homotopy groups of spheres localized at some prime ''p''. It is described in more detail in and . It is related to the EHP long exact sequence of ; the name "EHP" comes from the fact that Whitehead named 3 of the maps of his sequence "E" (the first letter of the German word "Einhängung" meaning "suspension"), "H" (for Hopf, as this map is the second Hopf-James invariant), and "P" (related to (Whitehead) products). For ''p'' = 2 the spectral sequence uses some exact sequences associated to the fibration :$S^n(2)\backslash rightarrow\; \backslash Omega\; S^(2)\backslash rightarrow\; \backslash Omega\; S^(2)$ (where Ω stands for a loop space and the (2) is localization of a topological space at the prime 2). This gives a spectral sequence with E1''k'',''n'' term π''k''+''n''(''S''2''n''−1(2)) and converging to π *''S''(2) (stable homotopy of spheres localized at 2). The spectral sequence has the advantage that the input is previously calculated homotopy groups. It was used by to calculate the first 31 stable homotopy groups of spheres. For arbitrary primes one uses some fibrations found by : :$\backslash widehat\; S^(p)\backslash rightarrow\; \backslash Omega\; S^(p)\backslash rightarrow\; \backslash Omega\; S^(p)$ :$S^(p)\backslash rightarrow\; \backslash Omega\; \backslash widehat\; S^(p)\backslash rightarrow\; \backslash Omega\; S^(p)$ where $\backslash widehat\; S^$ is the 2''np'' − 1 skeleton of the loop space $\backslash Omega\; S^$. (For ''p'' = 2, $\backslash widehat\; S^$ is the same as $S^$, so Toda's fibrations at ''p'' = 2 are the same as the James fibrations.) ==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「EHP spectral sequence」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.