A new metric criterion for non-amenability III: Non-amenability of R.Thompson's group F

TL;DR

This paper introduces new metric criteria for non-amenability and applies them to prove that R. Thompson's group F is non-amenable, advancing understanding of group properties.

Contribution

It develops novel metric criteria for non-amenability and demonstrates their effectiveness by proving R. Thompson's group F is non-amenable.

Findings

Proves R. Thompson's group F is non-amenable

Introduces new metric criteria for non-amenability

Provides applications of these criteria in group theory

Abstract

We present new metric criteria for non-amenability and discuss applications. The main application of the results of this paper is the proof of non-amenability of R.Thompson's group F. This is a continuation of the series of papers on our criteria for non-amenability. The current paper is independent of other papers in the series.