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arXiv · 2502.03180

Dehn functions of subgroups of products of free groups. Part II: Precise computations

Dario Ascari·Federica Bertolotti·Giovanni Italiano·Claudio Llosa Isenrich·Matteo Migliorini
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Abstract

We prove that the Bridson-Dison group has quartic Dehn function, thereby providing the first precise computation of the Dehn function of a subgroup of a direct product of free groups with super-quadratic Dehn function. We also prove that coabelian subgroups of direct products of $n$ free groups of finiteness type $\mathcal{F}_{n-1}$ and of corank $r\leq n-2$ have quadratic Dehn functions.

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Dario Ascari, Federica Bertolotti, Giovanni Italiano, Claudio Llosa Isenrich, Matteo Migliorini. 2025-02-05. Dehn functions of subgroups of products of free groups. Part II: Precise computations. https://arxiv.org/abs/2502.03180

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