Complete classification of the Dehn functions of Bestvina-Brady groups
arXiv:2507.07566 · doi:10.1007/s00039-026-00731-7
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.
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