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About: Rips machine

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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 It was introduced in unpublished work of Eliyahu Rips in about 1991.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 Morgan and Shalen that any finitely generated group acting freely on an R-tree is a free product of free abelian and surface groups.

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  • 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 It was introduced in unpublished work of Eliyahu Rips in about 1991.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 Morgan and Shalen that any finitely generated group acting freely on an R-tree is a free product of free abelian and surface groups. (en)
  • 在中，Rips machine是研究R-樹上的群作用的一個方法。這是於1991年左右在未發表的工作中引入的。 一個R-樹是唯一地的度量空間，內裏每條弧都與一個實區間等距。Rips證明了)的猜想，就是每個自由作用在R-樹上的有限生成群都是自由阿貝爾群和曲面群的自由積（）。 (zh)
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  • 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 It was introduced in unpublished work of Eliyahu Rips in about 1991.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 Morgan and Shalen that any finitely generated group acting freely on an R-tree is a free product of free abelian and surface groups. (en)
  • 在中，Rips machine是研究R-樹上的群作用的一個方法。這是於1991年左右在未發表的工作中引入的。 一個R-樹是唯一地的度量空間，內裏每條弧都與一個實區間等距。Rips證明了)的猜想，就是每個自由作用在R-樹上的有限生成群都是自由阿貝爾群和曲面群的自由積（）。 (zh)
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  • Rips machine (en)
  • Rips machine (zh)
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