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arXiv · 2507.07566

Complete classification of the Dehn functions of Bestvina-Brady groups

Yu-Chan Chang·Jerónimo García-Mejía·Matteo Migliorini
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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.

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Yu-Chan Chang, Jerónimo García-Mejía, Matteo Migliorini. 2025-07-10. Complete classification of the Dehn functions of Bestvina-Brady groups. https://doi.org/10.1007/s00039-026-00731-7

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