Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: The 2-components of the 31-stem homotopy groups of the 9 and 10-spheres   Group structures of the 2-primary components of the 31-stem homotopy groups
of spheres were studied by Oda in 1979. There are, however, two incompletely
determined groups. In this paper, our investigation with Toda's composition
method gives structures of them.

14
The categories of this paper are: math-ph
26
The categories of this paper are: bayes-an
35
The categories of this paper are: mtrl-th
25
The categories of this paper are: patt-sol
18
The categories of this paper are: econ
19
The categories of this paper are: eess
7
The categories of this paper are: hep-th
24
The categories of this paper are: dg-ga
12
The categories of this paper are: nucl-th
21
The categories of this paper are: adap-org
36
The categories of this paper are: cmp-lg
33
The categories of this paper are: plasm-ph
11
The categories of this paper are: hep-lat
28
The categories of this paper are: alg-geom
1
The categories of this paper are: cs
9
The categories of this paper are: nlin