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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 iterated monodromy group ： ウィキペディア英語版 iterated monodromy group In geometric group theory and dynamical systems the iterated monodromy group of a covering map is a group describing the monodromy action of the fundamental group on all iterations of the covering. A single covering map between spaces is therefore used to create a tower of coverings, by placing the covering over itself repeatedly. In terms of the Galois theory of covering spaces, this construction on spaces is expected to correspond to a construction on groups. The iterated monodromy group provides this construction, and it is applied to encode the combinatorics and symbolic dynamics of the covering, and provide examples of self-similar groups. ==Definition== The iterated monodromy group of ''f'' is the following quotient group: :$\backslash mathrmf\; :=\; \backslash frac\backslash ,\backslash digamma^n\}$ where : *$f:X\_1\backslash rightarrow\; X$ is a covering of a path-connected and locally path-connected topological space ''X'' by its subset $X\_1$, * $\backslash pi\_1\; (X,\; t)$ is the fundamental group of ''X'' and * $\backslash digamma\; :\backslash pi\_1\; (X,\; t)\backslash rightarrow\; \backslash mathrm\backslash ,f^(t)$ is the monodromy action for ''f''. * $\backslash digamma^n:\backslash pi\_1\; (X,\; t)\backslash rightarrow\; \backslash mathrm\backslash ,f^(t)$ is the monodromy action of the $n^\backslash mathrm$ iteration of ''f'', $\backslash forall\; n\backslash in\backslash mathbb\_0$. 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「iterated monodromy group」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.