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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 Torsion coefficient (topology) ： ウィキペディア英語版 Torsion coefficient (topology) In topology, a mathematical discipline, a torsion coefficient originated as an invariant characteristic of a manifold or hyper-surface. It is a measure of the degree of inherent twist or torsion in the manifold. Torsion coefficients were introduced with the theory of homology by the French mathematician Henri Poincaré around 1900.〔Erhard Scholz (Ed. I.M. James, 1999), Page 45: "In the end Poincaré had achieved a lot for a homological theory of (differentiable compact) manifolds about the turn of the century. He had introduced the old invariants (Betti numbers) in a new, much clearer symbolical framework, had introduced new ones (torsion coefficients)..."〕 Since then, homology and its torsion coefficients have found applications elsewhere. ==Topological invariants== The Betti numbers and torsion coefficients for a manifold are invariants which fully characterise its topology. Manifolds may be broadly divided into those with and without torsion.〔 Erhard Scholz (Ed. I.M. James 1999), page 45: "Poincare (1900) presented a new definition and a calculus for the calculation of Betti numbers and torsion coefficients.... That allowed him to read off immediately the Betti numbers and torsion coefficients and the distinction between manifolds 'with' or 'without' torsion...."〕 Where the Euler characteristic and orientability traditionally characterise a two-dimensional manifold, the Betti numbers and torsion coefficients may be understood as more sophisticated generalisations respectively of the Euler value and orientability. 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「Torsion coefficient (topology)」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.