Tree-graded asymptotic cones

  • Alessandro Sisto

    ETH Zürich, 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.

Cite this article

Alessandro Sisto, Tree-graded asymptotic cones. Groups Geom. Dyn. 7 (2013), no. 3, pp. 697–735

DOI 10.4171/GGD/203