Diophantine geometry over groups VII: The elementary theory of a hyperbolic group

By Z. Sela. 2009

133 citations recorded by the source corpus.

Subfields: Geometry and Topology, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/2f42bb6c1775cdc929833fc6a7eca6372bb3a599

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Geometry and Topology

1. Vincent Guirardel
2. Alexei G. Myasnikov
3. E. Daniyarova
4. Gilbert Levitt
5. Vladimir Nikanorovich Remeslennikov
6. D. Groves
7. Abderezak Ould Houcine
8. Denis V. Osin

In Mathematical Physics

1. Vincent Guirardel
2. Alexei G. Myasnikov
3. Gilbert Levitt
4. E. Daniyarova
5. Vladimir Nikanorovich Remeslennikov
6. D. Groves
7. Abderezak Ould Houcine
8. Denis V. Osin

Citations in the corpus

• Algebraic geometry over algebraic structures III: Equationally Noetherian property and compactness (2010, background): “e were a lot of papers on algebraic geometry over concrete groups, algebras, monoids and so on. Among them there are the famous works by O.G.Kharlampovich, 2 A.G.Myasnikov [14, 15, 16, 17] and Z.Sela [25, 26, 27] on algebraic geometry over free groups. In recent years we have achieved more general a”
• Homogeneity and prime models in torsion-free hyperbolic groups (2010, methodology): “([39, Definition 7.3]) Let Γ be a noncyclic torsion-free hyperbolic group.”
• Limit groups for relatively hyperbolic groups. I. The basic tools (2004, methodology): “that Sela gave was in terms on an action of G on an R-tree induced by the sequence {hn : G ! F}. Sela’s geometric definition also makes sense for -hyperbolic groups (see [ 42 ]).”
• Trees of cylinders and canonical splittings (2008, background): “Since CSA is a closed property in the space of marked groups, -limit groups for torsion-free hyperbolic are CSA ([ Sel02 ]); als o see [Cha00] for wilder examples.”