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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 monodromy ： ウィキペディア英語版 monodromy In mathematics, monodromy is the study of how objects from mathematical analysis, algebraic topology, algebraic geometry and differential geometry behave as they 'run round' a singularity. As the name implies, the fundamental meaning of ''monodromy'' comes from 'running round singly'. It is closely associated with covering maps and their degeneration into ramification; the aspect giving rise to monodromy phenomena is that certain functions we may wish to define fail to be ''single-valued'' as we 'run round' a path encircling a singularity. The failure of monodromy is best measured by defining a monodromy group: a group of transformations acting on the data that encodes what does happen as we 'run round'. ==Definition== Let ''X'' be a connected and locally connected based topological space with base point ''x'', and let $p:\backslash tilde\backslash to\; X$ be a covering with fiber $F\; =\; p^(x)$. For a loop based at ''x'', denote a lift under the covering map (starting at a point $\backslash tilde\backslash in\; F$) by $\backslash tilde$. Finally, we denote by $\backslash tilde\backslash cdot\backslash gamma$ the endpoint $\backslash tilde(1)$, which is generally different from $\backslash tilde$. There are theorems which state that this construction gives a well-defined group action of the fundamental group π1(''X'', ''x'') on ''F'', and that the stabilizer of $\backslash tilde$ is exactly $p\_(\backslash pi\_1(\backslash tilde,\backslash tilde))$, that is, an element () fixes a point in ''F'' if and only if it is represented by the image of a loop in $\backslash tilde$ based at $\backslash tilde$. This action is called the monodromy action and the corresponding homomorphism π1(''X'', ''x'') → Aut(''H'' *(''Fx'')) into the automorphism group on ''F'' is the algebraic monodromy. The image of this homomorphism is the monodromy group. There is another map π1(''X'', ''x'') → Diff(''Fx'')/Is(''Fx'') whose image is called the geometric monodromy group. 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「monodromy」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.