Notes on uniform exponential growth and Tits alternative

TL;DR

This paper discusses advances in uniform exponential growth and the Tits alternative, presenting improved theorems and results based on collaborations, with implications for group theory and geometric group theory.

Contribution

It provides new, improved versions of the Eskin-Mozes-Oh theorem and a uniform Tits alternative, advancing understanding of growth properties in groups.

Findings

Enhanced bounds for uniform exponential growth.

A uniform version of the Tits alternative.

Improved theorems with broader applicability.

Abstract

These notes contain results concerning uniform exponential growth which were obtained in collaborations with E. Breuillard and A. Salehi-Golsefidy, mostly during 2005, improving Eskin-Mozes-Oh theorem \cite{EMO}, as well as a uniform uniform version of Tits alternative improving \cite{uti}.