Instruct: Identify the main and secondary category of Arxiv papers based on the titles
Query: Homotopy types of spaces of submanifolds of ${\mathbb R}^n$
0
The categories of this paper are: hep-ph
6
The categories of this paper are: astro-ph
36
The categories of this paper are: cmp-lg
21
The categories of this paper are: adap-org
18
The categories of this paper are: econ
17
The categories of this paper are: q-fin
8
The categories of this paper are: hep-ex
32
The categories of this paper are: atom-ph
5
The categories of this paper are: gr-qc
33
The categories of this paper are: plasm-ph
7
The categories of this paper are: hep-th
3
The categories of this paper are: physics
24
The categories of this paper are: dg-ga
11
The categories of this paper are: hep-lat
23
The categories of this paper are: solv-int
25
The categories of this paper are: patt-sol