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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 Dehn twist ： ウィキペディア英語版 Dehn twist In geometric topology, a branch of mathematics, a Dehn twist is a certain type of self-homeomorphism of a surface (two-dimensional manifold). ==Definition== Suppose that ''c'' is a simple closed curve in a closed, orientable surface ''S''. Let ''A'' be a tubular neighborhood of ''c''. Then ''A'' is an annulus and so is homeomorphic to the Cartesian product of :$S^1\; \backslash times\; I,$ where ''I'' is the unit interval. Give ''A'' coordinates (''s'', ''t'') where ''s'' is a complex number of the form :$e^\; \backslash theta\}$ with :$\backslash theta\; \backslash in\; (),$ and ''t'' in the unit interval. Let ''f'' be the map from ''S'' to itself which is the identity outside of ''A'' and inside ''A'' we have :$\backslash displaystyle\; f(s,t)\; =\; (s\; e^\; 2\; \backslash pi\; t\},\; t).$ Then ''f'' is a Dehn twist about the curve ''c''. Dehn twists can also be defined on a non-orientable surface ''S'', provided one starts with a 2-sided simple closed curve ''c'' on ''S''. 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「Dehn twist」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.