Volume 9, issue 3 (2009)

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Limit groups for relatively hyperbolic groups. {I}. The basic tools

Daniel Groves

Algebraic & Geometric Topology 9 (2009) 1423–1466
Abstract

We begin the investigation of Γ–limit groups, where Γ is a torsion-free group which is hyperbolic relative to a collection of free abelian subgroups. Using the results of Druţu and Sapir [Topology 44 (2005) 959-1058], we adapt the results from the author’s paper [Algebr. Geom. Topol. 5 (2005) 1325-1364]. Specifically, given a finitely generated group G and a sequence of pairwise nonconjugate homomorphisms {hn: G Γ}, we extract an –tree with a nontrivial isometric G–action.

We then provide an analogue of Sela’s shortening argument.

Keywords
relatively hyperbolic group, limit group
Mathematical Subject Classification 2000
Primary: 20F65
Secondary: 20F67, 20E08, 57M07
References
Publication
Received: 20 March 2008
Revised: 17 December 2008
Accepted: 14 May 2009
Published: 26 July 2009
Authors
Daniel Groves
Department of Mathematics
University of Illinois at Chicago
851 S Morgan St
Chicago, IL 60607-7045
USA
http://www.math.uic.edu/~groves