Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Distortion for Abelian Subgroups of $\mathrm{Out}(F_n)$   We prove that abelian subgroups of the outer automorphism group of a free
group are quasi-isometrically embedded. Our proof uses recent developments in
the theory of train track maps by Feighn-Handel. As an application, we prove
the rank conjecture for $\mathrm{Out}(F_n)$.

28
The categories of this paper are: alg-geom
31
The categories of this paper are: ao-sci
4
The categories of this paper are: cond-mat
34
The categories of this paper are: chem-ph
3
The categories of this paper are: physics
1
The categories of this paper are: cs
10
The categories of this paper are: q-bio
21
The categories of this paper are: adap-org
15
The categories of this paper are: nucl-ex
11
The categories of this paper are: hep-lat
35
The categories of this paper are: mtrl-th
24
The categories of this paper are: dg-ga
6
The categories of this paper are: astro-ph
9
The categories of this paper are: nlin
33
The categories of this paper are: plasm-ph
18
The categories of this paper are: econ