Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: $\mathbb Z_{/p}\times \mathbb Z_{/p}$ actions on $S^n\times S^n$   We determine the homotopy type of quotients of $S^n \times S^n$ by free
actions of $\mathbb Z_{/p} \times \mathbb Z_{/p}$ where $2p>n+3$. Much like
free $\mathbb Z_{/p}$ actions, they can be classified via the first
$p$-localized $k$-invariant, but there are restrictions on the possibilities,
and these restrictions are sufficient to determine every possibility in the
$n=3$ case. We use this to complete the classification of free $\mathbb Z_{/p}
\times \mathbb Z_{/p}$ actions on $S^3 \times S^3$, for $p>3$, by reducing the
problem to the simultaneous classification of pairs of binary quadratic forms.
Although the restrictions are not sufficient to determine which $k$-invariants
are realizable in general, they can sometimes be used to rule out free actions
by groups that contain $\mathbb Z_{/p}\times\mathbb Z_{/p}$ as a normal Abelian
subgroup.

20
The categories of this paper are: acc-phys
31
The categories of this paper are: ao-sci
30
The categories of this paper are: q-alg
0
The categories of this paper are: hep-ph
9
The categories of this paper are: nlin
17
The categories of this paper are: q-fin
36
The categories of this paper are: cmp-lg
29
The categories of this paper are: funct-an
37
The categories of this paper are: supr-con
4
The categories of this paper are: cond-mat
14
The categories of this paper are: math-ph
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
11
The categories of this paper are: hep-lat
24
The categories of this paper are: dg-ga