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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 Rips machine ： ウィキペディア英語版 Rips machine In geometric group theory, the Rips machine is a method of studying the action of groups on R-trees. It was introduced in unpublished work of Eliyahu Rips in about 1991. An R-tree is a uniquely arcwise-connected metric space in which every arc is isometric to some real interval. Rips proved the conjecture of that any finitely generated group acting freely on an R-tree is a free product of free abelian and surface groups . ==Actions of surface groups on R-trees== By Bass–Serre theory, a group acting freely on a simplicial tree is free. This is no longer true for R-trees, as showed that the fundamental groups of surfaces of Euler characteristic less than −1 also act freely on a R-trees. They proved that the fundamental group of a connected closed surface S acts freely on an R-tree if and only if S is not one of the 3 nonorientable surfaces of Euler characteristic ≥−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「Rips machine」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.