Tree-graded asymptotic cones

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1 Citation (Scopus)

Abstract

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.

Original languageEnglish
Pages (from-to)697-735
Number of pages39
JournalGroups, Geometry, and Dynamics
Volume7
Issue number3
DOIs
Publication statusPublished - 27 Aug 2013

Keywords

  • Asymptotic cone
  • Relatively hyperbolic
  • Tree-graded

ASJC Scopus subject areas

  • Geometry and Topology
  • Discrete Mathematics and Combinatorics

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