Assouad--Nagata dimension of systolic complexes with almost flat intervals

Abstract

We introduce the notion of systolic complexes with almost flat intervals. They constitute a subclass of fit systolic complexes and arise naturally in the study of graphical C(3)--T(6) small cancellation complexes. We prove that their Assouad--Nagata dimension is bounded above by a universal constant. As consequences, we obtain universal bounds on the Assouad--Nagata dimension of tame simply connected graphical C(3)--T(6) small cancellation complexes and of finitely generated groups defined by graphical C(3)--T(6) small cancellation presentations. In the appendix, we observe that the proof of finiteness of asymptotic dimension for buildings due to Dymara and Schick also yields finiteness of their asymptotic Assouad--Nagata dimension.