A new metric criterion for non-amenability I

TL;DR

This paper introduces a new metric criterion for non-amenability based on traveling salesman groups, providing a concise proof of non-amenability for certain free Burnside groups.

Contribution

It presents a novel metric criterion for non-amenability and applies it to prove non-amenability of free Burnside groups with large odd exponents.

Findings

New metric criterion for non-amenability

Concise proof for free Burnside groups' non-amenability

Applicable to groups with large odd exponents

Abstract

By studying the so-called traveling salesman groups, we obtain a new metric criterion for non-amenability. As an application, we give a new and very short proof of non-amenability of free Burnside groups with sufficiently big odd exponent.