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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 Volume conjecture ： ウィキペディア英語版 Volume conjecture In the branch of mathematics called knot theory, the volume conjecture is the following open problem that relates quantum invariants of knots to the hyperbolic geometry of knot complements. Let ''O'' denote the unknot. For any knot ''K'' let $\backslash langle\; K\backslash rangle\_N$ be Kashaev's invariant of $K$; this invariant coincides with the following evaluation of the $N$-colored Jones polynomial $J\_(q)$ of $K$: : \frac.|}} Then the volume conjecture states that : where vol(''K'') denotes the hyperbolic volume of the complement of ''K'' in the 3-sphere. == Kashaev's Observation == observed that the asymptotic behavior of a certain state sum of knots gives the hyperbolic volume $\backslash operatorname(K)$ of the complement of knots $K$ and showed that it is true for the knots $4\_1$, $5\_2$ and $6\_1$. He conjectured that for the general hyperbolic knots the formula (2) would hold. His invariant for a knot $K$ is based on the theory of quantum dilogarithms at the $N$-th root of unity, $q=\backslash exp$. 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「Volume conjecture」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.