Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Relative outer automorphisms of free groups   Let $A_1,...,A_k$ be a system of free factors of $F_n$. The group of relative
automorphisms $Aut(F_n;A_1,...,A_k)$ is the group given by the automorphisms of
$F_n$ that restricted to each $A_i$ are conjugations by elements in $F_n$. The
group of relative outer automorphisms is defined as $Out(F_n;A_1,...,A_k) =
Aut(F_n;A_1,...,A_k)/Inn(F_n)$, where $Inn(F_n)$ is the normal subgroup of
$Aut(F_n)$ given by all the inner automorphisms. We define a contractible space
on which $Out(F_n;A_1,...,A_k)$ acts with finite stabilizers and we compute the
virtual cohomological dimension of this group.

18
The categories of this paper are: econ
10
The categories of this paper are: q-bio
13
The categories of this paper are: quant-ph
12
The categories of this paper are: nucl-th
7
The categories of this paper are: hep-th
29
The categories of this paper are: funct-an
19
The categories of this paper are: eess
35
The categories of this paper are: mtrl-th
31
The categories of this paper are: ao-sci
15
The categories of this paper are: nucl-ex
16
The categories of this paper are: stat
20
The categories of this paper are: acc-phys
33
The categories of this paper are: plasm-ph
3
The categories of this paper are: physics
17
The categories of this paper are: q-fin
22
The categories of this paper are: chao-dyn