Metric criteria for fixed price of countable groups

Fuente: arXiv
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Main Authors: Bevilacqua, Erin, Bowen, Lewis
Format: Preprint
Published: 2025
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author Bevilacqua, Erin
Bowen, Lewis
author_facet Bevilacqua, Erin
Bowen, Lewis
contents We establish general criteria for a countable group $Γ$ to have fixed price 1 depending on a choice of left-invariant proper metric on $Γ$. We apply this criterion to show that if $Γ_1,Γ_2$ are two countable groups satisfying a certain growth condition then $Γ_1\times Γ_2$ has fixed price 1. For example, $Γ\times Γ$ has fixed price 1 for any countable group $Γ$.
format Preprint
id arxiv_https___arxiv_org_abs_2510_05459
institution arXiv
publishDate 2025
record_format arxiv
spellingShingle Metric criteria for fixed price of countable groups
Bevilacqua, Erin
Bowen, Lewis
Group Theory
Dynamical Systems
We establish general criteria for a countable group $Γ$ to have fixed price 1 depending on a choice of left-invariant proper metric on $Γ$. We apply this criterion to show that if $Γ_1,Γ_2$ are two countable groups satisfying a certain growth condition then $Γ_1\times Γ_2$ has fixed price 1. For example, $Γ\times Γ$ has fixed price 1 for any countable group $Γ$.
title Metric criteria for fixed price of countable groups
topic Group Theory
Dynamical Systems
url https://arxiv.org/abs/2510.05459