High Dimensional Expanders and Property Testing

TL;DR

This paper establishes a connection between high dimensional expansion in simplicial complexes and property testing, showing that high dimensional expanders can be characterized by testable properties and deriving related results.

Contribution

It introduces a novel link between high dimensional expansion and property testing, providing new testability results for simplicial complexes.

Findings

High dimensional expanders are characterized by testable properties.

The paper derives several new testability results for simplicial complexes.

It bridges concepts from geometric group theory and property testing.

Abstract

We show that the high dimensional expansion property as defined by Gromov, Linial and Meshulam, for simplicial complexes is a form of testability. Namely, a simplicial complex is a high dimensional expander iff a suitable property is testable. Using this connection, we derive several testability results.