Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: S_3 x S_3 acts freely on S^3 x S^3   A free action of the direct product of two copies of the symmetric group on 3
elements on the cartesian product of two copies of the 3-sphere is constructed.
This nonlinear action is constructed using surgery. The action provides a
counterexample to a conjecture of Lewis made in 1968.

28
The categories of this paper are: alg-geom
30
The categories of this paper are: q-alg
22
The categories of this paper are: chao-dyn
19
The categories of this paper are: eess
10
The categories of this paper are: q-bio
12
The categories of this paper are: nucl-th
15
The categories of this paper are: nucl-ex
32
The categories of this paper are: atom-ph
21
The categories of this paper are: adap-org
25
The categories of this paper are: patt-sol
20
The categories of this paper are: acc-phys
33
The categories of this paper are: plasm-ph
18
The categories of this paper are: econ
35
The categories of this paper are: mtrl-th
1
The categories of this paper are: cs
8
The categories of this paper are: hep-ex