Geometric group theory | Trees (topology) | Hyperbolic geometry

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 It was introduced in unpublished work of Eliyahu Rips in about 1991.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

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Geometric group theory | Geometric topology | Finitely generated group | Metric space | Teichmüller space | Kleinian group | Geometrization conjecture | Real tree | Haken manifold | Bass–Serre theory | Euler characteristic | Ultralimit | Free product | Group (mathematics)