Two-Dimensional Systolic Complexes Satisfy Property A

TL;DR

This paper proves that 2-dimensional systolic complexes satisfy Property A by demonstrating their quasi-isometry to quadric complexes with flat intervals and applying a specific weight function.

Contribution

It establishes that 2-dimensional systolic complexes have Property A, linking their geometric structure to a key property in coarse geometry.

Findings

2-dimensional systolic complexes are quasi-isometric to quadric complexes with flat intervals

They satisfy Property A using the weight function of Brodzki et al.

The result connects systolic complexes to coarse geometric properties.

Abstract

We show that 2-dimensional systolic complexes are quasi-isometric to quadric complexes with flat intervals. We use this fact along with the weight function of Brodzki, Campbell, Guentner, Niblo and Wright to prove that 2-dimensional systolic complexes satisfy Property A.