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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 Gromov norm ： ウィキペディア英語版 Gromov norm In mathematics, the Gromov norm (or simplicial volume) of a compact oriented ''n''-manifold is a norm on the homology (with real coefficients) given by minimizing the sum of the absolute values of the coefficients over all singular chains representing a cycle. The Gromov norm of the manifold is the Gromov norm of the fundamental class.〔.〕〔.〕 It is named after Mikhail Gromov, who with William Thurston, proved that the Gromov norm of a finite volume hyperbolic ''n''-manifold is proportional to the hyperbolic volume.〔 Thurston also used the Gromov norm to prove that hyperbolic volume decreases under hyperbolic Dehn surgery.〔, pp. 196ff.〕 ==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「Gromov norm」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.