Complete classification of the Dehn functions of Bestvina-Brady groups
Group Theory
2026-01-01 v2 Geometric Topology
Abstract
We prove that the Dehn function of every finitely presented Bestvina-Brady group grows as a linear, quadratic, cubic, or quartic polynomial. In fact, we provide explicit criteria on the defining graph to determine the degree of this polynomial. As a consequence, we identify an obstruction that prevents certain Bestvina-Brady groups from admitting a CAT(0) structure.
Keywords
Cite
@article{arxiv.2507.07566,
title = {Complete classification of the Dehn functions of Bestvina-Brady groups},
author = {Yu-Chan Chang and Jerónimo García-Mejía and Matteo Migliorini},
journal= {arXiv preprint arXiv:2507.07566},
year = {2026}
}
Comments
Minor changes in various places. Example 4.11 has been added, and the proof of Proposition 5.8 now includes additional details. To appear in GAFA