Volume 9, issue 4 (2005)

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ISSN (electronic): 1364-0380
ISSN (print): 1465-3060
Limit groups for relatively hyperbolic groups, II: Makanin-Razborov diagrams

Daniel Groves

Geometry & Topology 9 (2005) 2319–2358

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