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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 Van Kampen diagram ： ウィキペディア英語版 Van Kampen diagram In the mathematical area of geometric group theory, a van Kampen diagram is a planar diagram used to represent the fact that a particular word in the generators of a group given by a group presentation represents the identity element in that group. ==History== The notion of a van Kampen diagram was introduced by Egbert van Kampen in 1933.〔E. van Kampen. (''On some lemmas in the theory of groups''. ) American Journal of Mathematics. vol. 55, (1933), pp. 268–273.〕 This paper appeared in the same issue of American Journal of Mathematics as another paper of van Kampen, where he proved what is now known as the Seifert–van Kampen theorem.〔E. R. van Kampen. ''On the connection between the fundamental groups of some related spaces''. American Journal of Mathematics, vol. 55 (1933), pp. 261–267.〕 The main result of the paper on van Kampen diagrams, now known as the ''van Kampen lemma'' can be deduced from the Seifert–van Kampen theorem by applying the latter to the presentation complex of a group. However, van Kampen did not notice it at the time and this fact was only made explicit much later (see, e.g.〔Aleksandr Yur'evich Ol'shanskii. ''Geometry of defining relations in groups.'' Translated from the 1989 Russian original by Yu. A. Bakhturin. Mathematics and its Applications (Soviet Series), 70. Kluwer Academic Publishers Group, Dordrecht, 1991. ISBN 0-7923-1394-1.〕). Van Kampen diagrams remained an underutilized tool in group theory for about thirty years, until the advent of the small cancellation theory in the 1960s, where van Kampen diagrams play a central role.〔Bruce Chandler, and Wilhelm Magnus. ''The history of combinatorial group theory. A case study in the history of ideas.'' Studies in the History of Mathematics and Physical Sciences, 9. Springer-Verlag, New York, 1982. ISBN 0-387-90749-1.〕 Currently van Kampen diagrams are a standard tool in geometric group theory. They are used, in particular, for the study of isoperimetric functions in groups, and their various generalizations such as isodiametric functions, filling length functions, and so on. 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「Van Kampen diagram」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.