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arXiv · 2501.01688

Explicit polynomial bounds on Dehn functions of subgroups of hyperbolic groups

Robert Kropholler·Claudio Llosa Isenrich·Ignat Soroko
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Abstract

In 1999 Brady constructed the first example of a non-hyperbolic finitely presented subgroup of a hyperbolic group by fibring a non-positively curved cube complex over the circle. We show that his example has Dehn function bounded above by $n^{96}$. This provides the first explicit polynomial upper bound on the Dehn function of a finitely presented non-hyperbolic subgroup of a hyperbolic group. We also determine the precise hyperbolicity constant for the $1$-skeleton of the universal cover of the cube complex in Brady's construction with respect to the $4$-point condition for hyperbolicity.

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Robert Kropholler, Claudio Llosa Isenrich, Ignat Soroko. 2025-01-03. Explicit polynomial bounds on Dehn functions of subgroups of hyperbolic groups. https://arxiv.org/abs/2501.01688

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