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arXiv · 2611.05763

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

Martín Blufstein·Victor Chepoi·Huaitao Gui·Damian Osajda
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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.

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Martín Blufstein, Victor Chepoi, Huaitao Gui, Damian Osajda. 2026-11-04. Assouad--Nagata dimension of systolic complexes with almost flat intervals. https://arxiv.org/abs/2611.05763

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