Conformal dimension of hyperbolic groups that split over elementary subgroups

Matias Carrasco; John M Mackay

doi:10.1007/s00222-021-01074-w

Conformal dimension of hyperbolic groups that split over elementary subgroups

Matias Carrasco, John M Mackay^*

^*Corresponding author for this work

Research output: Contribution to journal › Article (Academic Journal) › peer-review

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Abstract

We study the (Ahlfors regular) conformal dimension of the boundary at infinity of Gromov hyperbolic groups which split over elementary subgroups. If such a group is not virtually free, we show that the conformal dimension is equal to the maximal value of the conformal dimension of the vertex groups, or 1, whichever is greater, and we characterise when the conformal dimension is attained. As a consequence, we are able to characterise which Gromov hyperbolic groups (without 2-torsion) have conformal dimension 1, answering a question of Bonk and Kleiner.

Original language	English
Number of pages	60
Journal	Inventiones Mathematicae
Early online date	6 Oct 2021
DOIs	https://doi.org/10.1007/s00222-021-01074-w
Publication status	E-pub ahead of print - 6 Oct 2021

Bibliographical note

Funding Information:
This research was supported in part by EPSRC grant EP/P010245/1 and the MathAMSUD project Geometry and Dynamics of Infinite Groups.

Publisher Copyright:
© 2021, The Author(s).

Keywords

20F67
30L10
51F99

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Optimal geometric structures for hyperbolic groups
Mackay, J. M. (Principal Investigator)
1/11/16 → 31/08/18
Project: Research

Cite this

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abstract = "We study the (Ahlfors regular) conformal dimension of the boundary at infinity of Gromov hyperbolic groups which split over elementary subgroups. If such a group is not virtually free, we show that the conformal dimension is equal to the maximal value of the conformal dimension of the vertex groups, or 1, whichever is greater, and we characterise when the conformal dimension is attained. As a consequence, we are able to characterise which Gromov hyperbolic groups (without 2-torsion) have conformal dimension 1, answering a question of Bonk and Kleiner.",

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AU - Mackay, John M

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N2 - We study the (Ahlfors regular) conformal dimension of the boundary at infinity of Gromov hyperbolic groups which split over elementary subgroups. If such a group is not virtually free, we show that the conformal dimension is equal to the maximal value of the conformal dimension of the vertex groups, or 1, whichever is greater, and we characterise when the conformal dimension is attained. As a consequence, we are able to characterise which Gromov hyperbolic groups (without 2-torsion) have conformal dimension 1, answering a question of Bonk and Kleiner.

AB - We study the (Ahlfors regular) conformal dimension of the boundary at infinity of Gromov hyperbolic groups which split over elementary subgroups. If such a group is not virtually free, we show that the conformal dimension is equal to the maximal value of the conformal dimension of the vertex groups, or 1, whichever is greater, and we characterise when the conformal dimension is attained. As a consequence, we are able to characterise which Gromov hyperbolic groups (without 2-torsion) have conformal dimension 1, answering a question of Bonk and Kleiner.

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KW - 51F99

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M3 - Article (Academic Journal)

SN - 0020-9910

JO - Inventiones Mathematicae

JF - Inventiones Mathematicae

ER -

Conformal dimension of hyperbolic groups that split over elementary subgroups

Abstract

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Keywords

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Optimal geometric structures for hyperbolic groups

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