Residually free groups do not admit a uniform polynomial isoperimetric function

Dehn functions of coabelian subgroups of direct products of groups

“…Considering that the Stallings–Bieri groups have quadratic Dehn functions, one may wonder if the same applies to SPFs. In general, this turns out to be far from true; indeed, there are SPFs satisfying arbitrarily large polynomial lower bounds on their Dehn functions [27]. However, we will now explain that the result does remain true for SPFs with sufficiently high regularity properties.…”

“…A first general study of Dehn functions of subgroups of direct products of groups was performed by Bridson [9] in the cocyclic case and by Dison [17] in the coabelian case. Other results in this area include the ones mentioned in the previous paragraph, as well as [27]. However, we are still far from a complete description of the Dehn functions that can arise, even if we assume that the $$G_i$$ are free groups and that $$K$$ is coabelian.…”

“…Dison also posed the stronger version of Question 1 whether the class of Dehn functions of SPFs satisfies a uniform polynomial upper bound. While Tessera and the second author gave a negative answer to the uniform version of Dison's question, their examples are not (virtually) coabelian [27]. This raises the following question: Question Is there a polynomial $$p(n)$$ such that $$\delta _G(n)\preccurlyeq p(n)$$ for all coabelian SPFs $$G$$?…”