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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 : where ''I'' is the unit interval. Give ''A'' coordinates (''s'', ''t'') where ''s'' is a complex number of the form : with : 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 : 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
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