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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 Alexander's theorem ： ウィキペディア英語版 Alexander's theorem In mathematics Alexander's theorem states that every knot or link can be represented as a closed braid. The theorem is named after James Waddell Alexander II, who published its proof in 1923. Braids were first considered as a tool of knot theory by Alexander. His theorem gives a positive answer to :is it always possible to transform a given knot into a closed braid? However, the correspondence between knots and braids is clearly not one-to-one: a knot may have many braid representations. For example, conjugate braids yield equivalent knots. This leads to a second fundamental question: :which closed braids represent the same knot type? That question is addressed in Markov's theorem, which gives ‘moves’ relating any two closed braids that represent the same knot. == 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「Alexander's theorem」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.