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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 Jones polynomial ： ウィキペディア英語版 Jones polynomial In the mathematical field of knot theory, the Jones polynomial is a knot polynomial discovered by Vaughan Jones in 1984. Specifically, it is an invariant of an oriented knot or link which assigns to each oriented knot or link a Laurent polynomial in the variable $t^$ with integer coefficients.〔JONES POLYNOMIALS, VOLUME AND ESSENTIAL KNOT SURFACES: A SURVEY ()〕 ==Definition by the bracket== Suppose we have an oriented link $L$, given as a knot diagram. We will define the Jones polynomial, $V(L)$, using Kauffman's bracket polynomial, which we denote by $\backslash langle~\backslash rangle$. Note that here the bracket polynomial is a Laurent polynomial in the variable $A$ with integer coefficients. First, we define the auxiliary polynomial (also known as the normalized bracket polynomial) :$X(L)\; =\; (-A^3)^\backslash langle\; L\; \backslash rangle$, where $w(L)$ denotes the writhe of $L$ in its given diagram. The writhe of a diagram is the number of positive crossings ($L\_$ in the figure below) minus the number of negative crossings ($L\_$). The writhe is not a knot invariant. $X(L)$ is a knot invariant since it is invariant under changes of the diagram of $L$ by the three Reidemeister moves. Invariance under type II and III Reidemeister moves follows from invariance of the bracket under those moves. The bracket polynomial is known to change by multiplication by $-A^$ under a type I Reidemeister move. The definition of the $X$ polynomial given above is designed to nullify this change, since the writhe changes appropriately by +1 or -1 under type I moves. Now make the substitution $A\; =\; t^$ in $X(L)$ to get the Jones polynomial $V(L)$. This results in a Laurent polynomial with integer coefficients in the variable $t^$. 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「Jones polynomial」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.