Instruct: Identify the main and secondary category of Arxiv papers based on the titles
Query: Existence of spectral gaps, covering manifolds and residually finite
  groups
31
The categories of this paper are: ao-sci
34
The categories of this paper are: chem-ph
13
The categories of this paper are: quant-ph
0
The categories of this paper are: hep-ph
19
The categories of this paper are: eess
16
The categories of this paper are: stat
26
The categories of this paper are: bayes-an
25
The categories of this paper are: patt-sol
17
The categories of this paper are: q-fin
5
The categories of this paper are: gr-qc
33
The categories of this paper are: plasm-ph
35
The categories of this paper are: mtrl-th
29
The categories of this paper are: funct-an
37
The categories of this paper are: supr-con
11
The categories of this paper are: hep-lat
9
The categories of this paper are: nlin