Explicit polynomial bounds on Dehn functions of subgroups of hyperbolic groups

Autor:	Kropholler, Robert, Isenrich, Claudio Llosa, Soroko, Ignat
Rok vydání:	2025
Předmět:	Mathematics - Group Theory Mathematics - Geometric Topology 20F67 20F65 20F69 20F06
Druh dokumentu:	Working Paper
Popis:	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. Comment: 21 pages, 19 figures
Databáze:	arXiv
Externí odkaz:	http://arxiv.org/abs/2501.01688 Zobrazit plný text záznamu View this record from Arxiv