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<p>We construct 4-dimensional CAT(0) groups containing finitely presented subgroups whose Dehn functions are exp<sup>(<i>n</i>)</sup>(<i>x</i><sup><i>m</i></sup>) for integers <i>n,m</i> ≥ 1 and 6-dimensional CAT(0) groups containing finitely presented subgroups whose Dehn functions are exp<sup>(<i>n</i>)</sup>(<i>x</i><sup><i>α</i></sup>) for integers <i>n</i> ≥ 1 and <i>α</i> dense in [1, ∞). This significantly expands the known geometric behavior of subgroups of CAT(0) groups.</p>

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Superexponential Dehn functions inside CAT(0) groups

  • 期刊论文

  • 发表日期：

    2025年11月25日

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  • Noel Brady,
  • Hung Cong Tran

摘要

We construct 4-dimensional CAT(0) groups containing finitely presented subgroups whose Dehn functions are exp(n)(xm) for integers n,m ≥ 1 and 6-dimensional CAT(0) groups containing finitely presented subgroups whose Dehn functions are exp(n)(xα) for integers n ≥ 1 and α dense in [1, ∞). This significantly expands the known geometric behavior of subgroups of CAT(0) groups.