Instruct: Identify the main and secondary category of Arxiv papers based on the titles
Query: $\eta$-invariant and a problem of B\'erard-Bergery on the existence of
  closed geodesics
10
The categories of this paper are: q-bio
0
The categories of this paper are: hep-ph
24
The categories of this paper are: dg-ga
29
The categories of this paper are: funct-an
17
The categories of this paper are: q-fin
6
The categories of this paper are: astro-ph
4
The categories of this paper are: cond-mat
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
7
The categories of this paper are: hep-th
26
The categories of this paper are: bayes-an
5
The categories of this paper are: gr-qc
1
The categories of this paper are: cs
37
The categories of this paper are: supr-con
28
The categories of this paper are: alg-geom