Instruct: Identify the main and secondary category of Arxiv papers based on the titles
Query: The homology of groups, profinite completions, and echoes of Gilbert
  Baumslag
22
The categories of this paper are: chao-dyn
25
The categories of this paper are: patt-sol
8
The categories of this paper are: hep-ex
13
The categories of this paper are: quant-ph
14
The categories of this paper are: math-ph
6
The categories of this paper are: astro-ph
19
The categories of this paper are: eess
3
The categories of this paper are: physics
7
The categories of this paper are: hep-th
26
The categories of this paper are: bayes-an
30
The categories of this paper are: q-alg
33
The categories of this paper are: plasm-ph
20
The categories of this paper are: acc-phys
28
The categories of this paper are: alg-geom
4
The categories of this paper are: cond-mat
11
The categories of this paper are: hep-lat