Instruct: Identify the main and secondary category of Arxiv papers based on the titles
Query: On the essential spectrum of complete non-compact manifolds
24
The categories of this paper are: dg-ga
27
The categories of this paper are: comp-gas
9
The categories of this paper are: nlin
16
The categories of this paper are: stat
12
The categories of this paper are: nucl-th
10
The categories of this paper are: q-bio
7
The categories of this paper are: hep-th
34
The categories of this paper are: chem-ph
22
The categories of this paper are: chao-dyn
11
The categories of this paper are: hep-lat
20
The categories of this paper are: acc-phys
17
The categories of this paper are: q-fin
3
The categories of this paper are: physics
8
The categories of this paper are: hep-ex
32
The categories of this paper are: atom-ph
0
The categories of this paper are: hep-ph