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Groups, Geometry, and Dynamics

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Volume 7, Issue 3, 2013, pp. 697–735
DOI: 10.4171/GGD/203

Published online: 2013-08-27

Tree-graded asymptotic cones

Alessandro Sisto[1]

(1) ETH Z├╝rich, Switzerland

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.

Keywords: Tree-graded, asymptotic cone, relatively hyperbolic

Sisto Alessandro: Tree-graded asymptotic cones. Groups Geom. Dyn. 7 (2013), 697-735. doi: 10.4171/GGD/203