Tree-graded asymptotic cones

Alessandro Sisto

doi:10.4171/GGD/203

Tree-graded asymptotic cones

Alessandro Sisto^*

^*Corresponding author for this work

Research output: Contribution to journal › Article › peer-review

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 language	English
Pages (from-to)	697-735
Number of pages	39
Journal	Groups, Geometry, and Dynamics
Volume	7
Issue number	3
DOIs	https://doi.org/10.4171/GGD/203
Publication status	Published - 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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10.4171/GGD/203

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AB - 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.

KW - Asymptotic cone

KW - Relatively hyperbolic

KW - Tree-graded

UR - http://www.scopus.com/inward/record.url?scp=84886878647&partnerID=8YFLogxK

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DO - 10.4171/GGD/203

M3 - Article

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IS - 3

ER -

Tree-graded asymptotic cones

Abstract

Keywords

ASJC Scopus subject areas

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