Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: The homotopy type of the space of degree 0 immersed plane curves   The space of all immersed closed curves of rotation degree 0 in the plane
modulo reparametrizations has the same homotopy groups as the circle times the
2-sphere.

35
The categories of this paper are: mtrl-th
30
The categories of this paper are: q-alg
10
The categories of this paper are: q-bio
24
The categories of this paper are: dg-ga
16
The categories of this paper are: stat
28
The categories of this paper are: alg-geom
18
The categories of this paper are: econ
32
The categories of this paper are: atom-ph
26
The categories of this paper are: bayes-an
6
The categories of this paper are: astro-ph
13
The categories of this paper are: quant-ph
4
The categories of this paper are: cond-mat
1
The categories of this paper are: cs
17
The categories of this paper are: q-fin
15
The categories of this paper are: nucl-ex
9
The categories of this paper are: nlin