Stability of Haagerup property under graph product

TL;DR

This paper proves that the Haagerup property is preserved when taking graph products of finitely many groups, each having this property, thus extending the understanding of how this property behaves under complex group constructions.

Contribution

The paper establishes that the Haagerup property is stable under graph product operations for finitely many groups, providing a significant extension of known results in geometric group theory.

Findings

Haagerup property preserved under graph products

Extension of stability results for the Haagerup property

Applicable to finitely many groups with this property

Abstract

In this paper, we prove that any graph product of finitely many groups, all satisfying the Haagerup property (or Gromov's a-T-menability) also satisfies Haagerup property.