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<p>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.</p>

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Complete Classification of the Dehn Functions of Bestvina–Brady Groups

  • 期刊论文

  • 出版模式：

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  • 发表日期：

    2026年2月2日

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  • Yu-Chan Chang,
  • Jerónimo García-Mejía,
  • Matteo Migliorini

摘要

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.