Group actions with commensurated subsets, wallings and cubings

TL;DR

This paper explores the relationship between group actions that preserve large subsets and geometric structures like wallings and cubings, linking algebraic properties to geometric and combinatorial frameworks.

Contribution

It introduces new connections between commensurating group actions and geometric structures such as wallings and CAT(0) cubings.

Findings

Establishes links between commensurating actions and wallings

Connects properties FW and PW to geometric structures

Analyzes implications for Schreier graphs

Abstract

We study commensurating actions of groups and the associated properties FW and PW, in connection with wallings, median graphs, CAT(0) cubings and multi-ended Schreier graphs.