Conformal Dimension And Random Groups

John M. Mackay*

*Corresponding author for this work

Research output: Contribution to journalArticle (Academic Journal)

7 Citations (Scopus)

Abstract

We give a lower and an upper bound for the conformal dimension of the boundaries of certain small cancellation groups.

We apply these bounds to the few relator and density models for random groups. This gives generic bounds of the following form, where l is the relator length, going to infinity.

(a) 1 + 1/C <Cdim(partial derivative(infinity)G) <Cl/log(l), for the few relator model, and

(b) 1 + l/(C log(l)) <Cdim(partial derivative(infinity)G) <Cl, for the density model, at densities d <1/16.

In particular, for the density model at densities d <1/16, as the relator length l goes to infinity, the random groups will pass through infinitely many different quasi-isometry classes.

Original languageEnglish
Pages (from-to)213-239
Number of pages27
JournalGeometric and Functional Analysis
Volume22
Issue number1
DOIs
Publication statusPublished - Feb 2012

Keywords

  • ONE-RELATOR GROUPS
  • random groups
  • RIGIDITY
  • BOUNDARY
  • Conformal dimension

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