Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Outer automorphism groups of free groups: linear and free
  representations   We study the existence of homomorphisms between Out(F_n) and Out(F_m) for n >
5 and m < n(n-1)/2, and conclude that if m is not equal to n then each such
homomorphism factors through the finite group of order 2. In particular this
provides an answer to a question of Bogopol'skii and Puga. In the course of the
argument linear representations of Out(F_n) in dimension less than n(n+1)/2
over fields of characteristic zero are completely classified. It is shown that
each such representation has to factor through the natural projection from
Out(F_n) to GL(n,Z) coming from the action of Out(F_n) on the abelianisation of
F_n. We obtain similar results about linear representation theory of Out(F_4)
and Out(F_5).

8
The categories of this paper are: hep-ex
30
The categories of this paper are: q-alg
13
The categories of this paper are: quant-ph
24
The categories of this paper are: dg-ga
11
The categories of this paper are: hep-lat
9
The categories of this paper are: nlin
16
The categories of this paper are: stat
7
The categories of this paper are: hep-th
23
The categories of this paper are: solv-int
35
The categories of this paper are: mtrl-th
20
The categories of this paper are: acc-phys
21
The categories of this paper are: adap-org
0
The categories of this paper are: hep-ph
12
The categories of this paper are: nucl-th
34
The categories of this paper are: chem-ph
3
The categories of this paper are: physics