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

Groves, Daniel¹

¹Department of Mathematics, University of Illinois at Chicago, 851 S Morgan St, Chicago, IL 60607-7045, USA

Algebraic and Geometric Topology, Tome 9 (2009) no. 3, pp. 1423-1466

Résumé

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 ℝ–tree with a nontrivial isometric G–action.

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

Détail

DOI : 10.2140/agt.2009.9.1423

Keywords: relatively hyperbolic group, limit group

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