Limit groups for relatively hyperbolic groups, II: Makanin-Razborov diagrams

By D. Groves. 2005

62 citations recorded by the source corpus.

Let be a torsion-free group which is hyperbolic relative to a collection of free abelian subgroups. We construct Makanin–Razborov diagrams for . We also prove that every system of equations over is equivalent to a finite subsystem, and a number of structural results about –limit groups.

Subfields: Geometry and Topology, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/8bfbd3253931a2e3d3ba62649eb72413a047f3a9

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In Geometry and Topology

In Mathematical Physics

Citations in the corpus

Unification theorems in algebraic geometry (2008, background): “…over G [4, 24, 25, 26, 47], groups universally equivalent to G [40, 13, 34], limit groups of G in the Grigorchuk-Gromov’s metric [10], in the theory of equations in groups [28, 38, 39, 24, 25, 26, 18], in group actions [8, 12, 35, 17, 14], in the solutions of Tarski problems [27, 48], etc.”
Algebraic geometry over algebraic structures III: Equationally Noetherian property and compactness (2010, background): “orem A and Theorem C give a description of coordinate algebras by means of limit algebras. The limit algebraic structures (groups, as the rule) become the object of intense interest in modern algebra [2, 5, 7, 8, 9, 10, 11]. Theorems A and C are formulated for so-called equationally Noetherian algeb”
Diophantine geometry over groups VII: The elementary theory of a hyperbolic group (2009, background): “In a sequence of papers Groves has studied systems of equations over torsion-free relatively hyperbolic groups with abelian parabolic groups [8].”
Krull dimension of solvable groups (2008, unknown): “G R ] 2 1 Contents”