This research demonstrates the growth of Dehn functions in Bestvina–Brady groups, suggesting structural implications.
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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Chang et al. (2026) studied this question.
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