Limit groups for relatively hyperbolic groups, I: The basic tools

Details Limit groups for relatively hyperbolic groups, I: The basic tools Limit groups for relatively hyperbolic groups, I: The basic tools

2004-12-24

arxiv.org/abs/math/0412492v2

Mathematics

Group Theory

41 pages. The new version of this paper has been substantially rewritten. It now includes all of the results of the previous v

Scientific paper

We begin the investigation of Gamma-limit groups, where Gamma is a torsion-free group which is hyperbolic relative to a collection of free abelian subgroups. Using the results of Drutu and Sapir, we adapt the results from math.GR/0404440 to this context. Specifically, given a finitely generated group G, and a sequence of pairwise non-conjugate homomorphisms {h_n : G -> Gamma}, we extract an R-tree with a nontrivial isometric G-action. We then prove an analogue of Sela's shortening argument.

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