Coboundary expanders

TL;DR

This paper extends the concept of edge expansion from graphs to higher-dimensional CW complexes and demonstrates that certain random complexes typically exhibit this coboundary expansion property.

Contribution

It introduces a topological generalization of edge expansion and proves its high-probability presence in specific random CW complexes.

Findings

Random complexes often have coboundary expansion

Extension of edge expansion to higher dimensions

High-probability properties in topological complexes

Abstract

We describe a natural topological generalization of edge expansion for graphs to regular CW complexes and prove that this property holds with high probability for certain random complexes.