An Invitation to the Lifting Decomposition in CAT(0) Cube Complexes

Explore the lifting decomposition in CAT(0) cube complexes through this 40-minute conference talk from the Workshop on "Geometric and Asymptotic Group Theory with Applications 2023 - Groups and Dynamics" at the Erwin Schrödinger International Institute. Delve into the extension of previous work by Caprace and Sageev, focusing on the simplicity and utility of this mathematical tool. Examine lifting decompositions associated with various natural objects in CAT(0) cube complexes and discover theorems proven using this approach. Cover key topics including Cat Zero complexes, discrete wall spaces, reversible partitions, consistency, projection, infinite compactified lines, and practical applications. Gain insights into the mathematical concepts and their relevance in geometric and asymptotic group theory.

Introduction
Cat Zero complexes
Discrete wall space
Reversible partitions
Applications
Consistency
Projection
Other sets
Infinite compactified lines
Other steps
Examples and uses
Second application
Key properties