A Short Proof of a Generalised Conjecture of Erdős in Amenable Groups

Author
Affiliation

Kai Prince

The University of Manchester

Abstract

Introduction

Preliminaries

Amenable Groups and Actions

Topological Dynamics of Group Actions

Recurrence Results & Ergodic Theorems

Erdős Cubes & Cubic Measures

Factor Maps

Key Dynamical Results

Proof of Theorem (ref)

Furstenberg’s Correspondence Princple

Kronecker Factor

Choosing a point \(x_1\)

The joining \(\nu\)

Proof Conclusion

Proof of Corollary (ref)

Proof of Theorem (ref)

Discussion