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2009 Limit groups for relatively hyperbolic groups. {I}. The basic tools
Daniel Groves
Algebr. Geom. Topol. 9(3): 1423-1466 (2009). 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 {hn:GΓ}, we extract an –tree with a nontrivial isometric G–action.

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

Citation

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Daniel Groves. "Limit groups for relatively hyperbolic groups. {I}. The basic tools." Algebr. Geom. Topol. 9 (3) 1423 - 1466, 2009. https://doi.org/10.2140/agt.2009.9.1423

Information

Received: 20 March 2008; Revised: 17 December 2008; Accepted: 14 May 2009; Published: 2009
First available in Project Euclid: 20 December 2017

zbMATH: 1231.20038
MathSciNet: MR2530123
Digital Object Identifier: 10.2140/agt.2009.9.1423

Subjects:
Primary: 20F65
Secondary: 20E08, 20F67, 57M07

Rights: Copyright © 2009 Mathematical Sciences Publishers

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