Bestvina-Brady群Dehn函数完整分类
群论
2026-01-01 v2 几何拓扑
摘要
我们证明了每个 finitely presented Bestvina-Brady 群的 Dehn 函数增长方式为线性、二次、三次或四次多项式。实际上，我们给出了基于定义图的判据，用于确定该多项式的次数。作为结果，我们识别出一种阻止某些 Bestvina-Brady 群具有 CAT(0) 结构的障碍。
引用
@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}
}
备注
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