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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 Kauffman polynomial ： ウィキペディア英語版 Kauffman polynomial In knot theory, the Kauffman polynomial is a 2-variable knot polynomial due to Louis Kauffman. It is initially defined on a link diagram as :$F(K)(a,z)=a^L(K)\backslash ,$ where $w(K)$ is the writhe of the link diagram and $L(K)$ is a polynomial in ''a'' and ''z'' defined on link diagrams by the following properties: *$L(O)\; =\; 1$ (O is the unknot) *$L(s\_r)=aL(s),\; \backslash qquad\; L(s\_\backslash ell)=a^L(s).$ *''L'' is unchanged under type II and III Reidemeister moves Here $s$ is a strand and $s\_r$ (resp. $s\_\backslash ell$) is the same strand with a right-handed (resp. left-handed) curl added (using a type I Reidemeister move). Additionally ''L'' must satisfy Kauffman's skein relation: : The pictures represent the ''L'' polynomial of the diagrams which differ inside a disc as shown but are identical outside. Kauffman showed that ''L'' exists and is a regular isotopy invariant of unoriented links. It follows easily that ''F'' is an ambient isotopy invariant of oriented links. The Jones polynomial is a special case of the Kauffman polynomial, as the ''L'' polynomial specializes to the bracket polynomial. The Kauffman polynomial is related to Chern-Simons gauge theories for SO(N) in the same way that the HOMFLY polynomial is related to Chern-Simons gauge theories for SU(N) (see Witten's article "Quantum field theory and the Jones polynomial", in Commun. Math. Phys.) ==Further reading== *Louis Kauffman, ''On Knots'', (1987), ISBN 0-691-08435-1 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「Kauffman 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.