Residually free groups do not admit a uniform polynomial isoperimetric function

Llosa Isenrich, Claudio; Tessera, Romain

doi:10.1090/proc/15082

Residually free groups do not admit a uniform polynomial isoperimetric function
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by Claudio Llosa Isenrich and Romain Tessera

Proc. Amer. Math. Soc. 148 (2020), 4203-4212

DOI: https://doi.org/10.1090/proc/15082

Published electronically: June 1, 2020

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Abstract:

We show that there is no uniform polynomial isoperimetric function for finitely presented subgroups of direct products of free groups by producing a sequence of subgroups $G_r\leq F_2^{(1)} \times \dots \times F_2^{(r)}$ of direct products of 2-generated free groups with Dehn functions bounded below by $n^{r}$. The groups $G_r$ are obtained from the examples of non-coabelian subdirect products of free groups constructed by Bridson, Howie, Miller, and Short. As a consequence we obtain that residually free groups do not admit a uniform polynomial isoperimetric function.

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