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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 Casson invariant ： ウィキペディア英語版 Casson invariant In 3-dimensional topology, a part of the mathematical field of geometric topology, the Casson invariant is an integer-valued invariant of oriented integral homology 3-spheres, introduced by Andrew Casson. Kevin Walker (1992) found an extension to rational homology 3-spheres, called the Casson–Walker invariant, and Christine Lescop (1995) extended the invariant to all closed oriented 3-manifolds. ==Definition== A Casson invariant is a surjective map λ from oriented integral homology 3-spheres to Z satisfying the following properties: *λ(S3) = 0. *Let Σ be an integral homology 3-sphere. Then for any knot ''K'' and for any integer ''n'', the difference ::$\backslash lambda\backslash left(\backslash Sigma+\backslash frac\backslash cdot\; K\backslash right)-\backslash lambda\backslash left(\backslash Sigma+\backslash frac\backslash cdot\; K\backslash right)$ :is independent of ''n''. Here $\backslash Sigma+\backslash frac\backslash cdot\; K$ denotes $\backslash frac$ Dehn surgery on Σ by ''K''. *For any boundary link ''K'' ∪ ''L'' in Σ the following expression is zero: ::$\backslash lambda\backslash left(\backslash Sigma+\backslash frac\backslash cdot\; K+\backslash frac\backslash cdot\; L\backslash right)\; -\backslash lambda\backslash left(\backslash Sigma+\backslash frac\backslash cdot\; K+\backslash frac\backslash cdot\; L\backslash right)-\backslash lambda\backslash left(\backslash Sigma+\backslash frac\backslash cdot\; K+\backslash frac\backslash cdot\; L\backslash right)\; +\backslash lambda\backslash left(\backslash Sigma+\backslash frac\backslash cdot\; K+\backslash frac\backslash cdot\; L\backslash right)$ The Casson invariant is unique (with respect to the above properties) up to an overall multiplicative constant. 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「Casson invariant」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.