Abstract
We begin the investigation of –limit groups, where 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 and a sequence of pairwise nonconjugate homomorphisms , we extract an –tree with a nontrivial isometric –action.
We then provide an analogue of Sela’s shortening argument.
Citation
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
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