Tree-graded asymptotic cones

Details Tree-graded asymptotic cones Tree-graded asymptotic cones

2012-04-03

arxiv.org/abs/1204.0682v1

Mathematics

Geometric Topology

Part of http://arxiv.org/abs/1010.4552v3, that has been split. To appear in Groups, Geometry and Dynamics

Scientific paper

We study the bilipschitz equivalence type of tree-graded spaces, showing that asymptotic cones of relatively hyperbolic groups (resp. asymptotic cones of groups containing a cut-point) only depend on the bilipschitz equivalence types of the pieces in the standard (resp. minimal) tree-graded structure. In particular, the asymptotic cones of many relatively hyperbolic groups do not depend on the scaling factor. We also describe the asymptotic cones as above "explicitly". Part of these results were obtained independently and simultaneously by D. Osin and M. Sapir.

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