Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: First cohomology groups of the automorphism group of a free group with
  coefficients in the abelianization of the IA-automorphism group   We compute a twisted first cohomology group of the automorphism group of a
free group with coefficients in the abelianization $V$ of the IA-automorphism
group of a free group. In particular, we show that it is generated by two
crossed homomorphisms constructed with the Magnus representation and the Magnus
expansion due to Morita and Kawazumi respectively. As a corollary, we see that
the first Johnson homomorphism does not extend to the automorphism group of a
free group as a crossed homomorphism for the rank of the free group is greater
than 4.

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The categories of this paper are: q-bio
1
The categories of this paper are: cs
36
The categories of this paper are: cmp-lg
5
The categories of this paper are: gr-qc
23
The categories of this paper are: solv-int
32
The categories of this paper are: atom-ph
9
The categories of this paper are: nlin
27
The categories of this paper are: comp-gas
37
The categories of this paper are: supr-con
15
The categories of this paper are: nucl-ex
11
The categories of this paper are: hep-lat
31
The categories of this paper are: ao-sci
20
The categories of this paper are: acc-phys
6
The categories of this paper are: astro-ph
18
The categories of this paper are: econ
26
The categories of this paper are: bayes-an