Groups, Orders, and Dynamics

TL;DR

This monograph explores the properties of left-orderable groups through various mathematical lenses, including dynamical, probabilistic, geometric, combinatorial, analytic, and topological perspectives, with recent updates and new results.

Contribution

It provides a comprehensive, mostly self-contained treatment of left-orderable groups, incorporating new results and improvements across multiple mathematical disciplines.

Findings

Enhanced understanding of left-orderable groups

Integration of dynamical and probabilistic methods

Inclusion of new results and corrections

Abstract

This is an almost self-contained monograph (containing some new results) on left-orderable groups which mostly rely on dynamical and probabilistic aspects, but also on geometric, combinatorial, analytic, and topological ones. This new version contains many improvements, corrections and updates, many of them suggested by the referees and colleagues along the last years.