Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Residually free groups do not admit a uniform polynomial isoperimetric
  function   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.

8
The categories of this paper are: hep-ex
3
The categories of this paper are: physics
14
The categories of this paper are: math-ph
18
The categories of this paper are: econ
7
The categories of this paper are: hep-th
20
The categories of this paper are: acc-phys
4
The categories of this paper are: cond-mat
12
The categories of this paper are: nucl-th
19
The categories of this paper are: eess
23
The categories of this paper are: solv-int
35
The categories of this paper are: mtrl-th
29
The categories of this paper are: funct-an
31
The categories of this paper are: ao-sci
10
The categories of this paper are: q-bio
9
The categories of this paper are: nlin
34
The categories of this paper are: chem-ph