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

Groves, Daniel

doi:10.2140/gt.2005.9.2319

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

Daniel Groves

Geometry & Topology 9 (2005) 2319–2358

DOI: 10.2140/gt.2005.9.2319

arXiv: math.GR/0503045

Abstract

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

Keywords

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

Mathematical Subject Classification 2000

Primary: 20F65

Secondary: 20F67, 20E08, 57M07

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Publication

Received: 15 March 2005

Accepted: 3 December 2005

Published: 21 December 2005

Proposed: Benson Farb

Seconded: Walter Neumann, Martin Bridson

Authors

Daniel Groves
Department of Mathematics California Institute of Technology Pasadena California 91125 USA

Volume 9, issue 4 (2005)