Algebraic & Geometric Topology 9 (2009) 1423–1466

DOI: 10.2140/agt.2009.9.1423

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 {h_n: G → Γ}, we extract an R–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

Primary: 20F65

Secondary: 20E08, 20F67, 57M07

References

Publication

Received: 20 March 2008
Revised: 17 December 2008
Accepted: 14 May 2009
Published: 26 July 2009

Authors