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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 Wirtinger presentation ： ウィキペディア英語版 Wirtinger presentation In mathematics, especially in group theory, a Wirtinger presentation is a finite presentation where the relations are of the form $wg\_iw^\; =\; g\_j$ where $w$ is a word in the generators, $\backslash$. Wilhelm Wirtinger observed that the exteriors of knots in 3-space have fundamental groups with presentations of this form. ==Preliminaries and definition== A ''knot'' ''K'' is an embedding of the one-sphere ''S''1 in three-dimensional space R3. (Alternatively, the ambient space can also be taken to be the three-sphere ''S''3, which does not make a difference for the purposes of the Wirtinger presentation.) The open subspace which is the complement of the knot, ''S''3 \ ''K'' is the knot complement. Its fundamental group ''π''1(''S''3 \ ''K'') is an invariant of the knot in the sense that equivalent knots have isomorphic knot groups. It is therefore interesting to understand this group in an accessible way. A ''Wirtinger presentation'' is derived from a regular projection of an oriented knot. Such a projection can be pictured as a finite number of (oriented) arcs in the plane, separated by the crossings of the projection. The fundamental group is generated by loops winding around each arc. Each crossing gives rise to a certain relation among the generators corresponding to the arcs meeting at the crossing. 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「Wirtinger presentation」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.