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

Groves, Daniel¹

¹ Department of Mathematics, California Institute of Technology, Pasadena, California 91125, USA

Geometry & topology, Tome 9 (2005) no. 4, pp. 2319-2358.

Résumé

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

Détail

DOI : 10.2140/gt.2005.9.2319

Keywords: relatively hyperbolic groups, limit groups, $\mathbb{R}$–trees

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