Group actions with commensurated subsets, wallings and cubings

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.

78 pages, no figure. Preliminary version, comments welcome! v1->v2 extended version: the new Section 7 was partly extracted from Section 3; some subsections are new (notably 4H and from 7B to 7F)

References in corpus (1)

• Group actions on median spaces

Cited by in corpus (14)

• The Median Class and Superrigidity of Actions on CAT(0) Cube Complexes
• Graphical small cancellation groups with the Haagerup property
• Locally compact wreath products
• Commensurating actions for groups of piecewise continuous transformations
• On the space of ends of infinitely generated groups
• Superrigidity of actions on finite rank median spaces
• Commensurating actions of birational groups and groups of pseudo-automorphisms
• Regularization of birational actions of FW groups
• Property FW and wreath products of groups: a simple approach using Schreier graphs
• Property FW, differentiable structures, and smoothability of singular actions
• Locally elliptic actions, torsion groups, and nonpositively curved spaces
• Hyperbolic and cubical rigidities of Thompson's group V
• Property FW and 1-dimensional piecewise groups
• Wreath products of groups acting with bounded orbits