Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: A construction of $G_2$-manifolds from K3 surfaces with a
  $\mathbb{Z}^2_2$-action   A product of a K3 surface $S$ and a flat 3-dimensional torus $T^3$ is a
manifold with holonomy $SU(2)$. Since $SU(2)$ is a subgroup of $G_2$, $S\times
T^3$ carries a torsion-free $G_2$-structure. We assume that $S$ admits an
action of $\mathbb{Z}^2_2$ with certain properties. There are several
possibilities to extend this action to $S\times T^3$. A recent result of Joyce
and Karigiannis allows us to resolve the singularities of $(S\times
T^3)/\mathbb{Z}^2_2$ such that we obtain smooth $G_2$-manifolds. We classify
the quotients $(S\times T^3)/\mathbb{Z}^2_2$ under certain restrictions and
compute the Betti numbers of the corresponding $G_2$-manifolds. Moreover, we
study a class of quotients by a non-abelian group. Several of our examples have
new values of $(b^2,b^3)$.

30
The categories of this paper are: q-alg
3
The categories of this paper are: physics
29
The categories of this paper are: funct-an
27
The categories of this paper are: comp-gas
32
The categories of this paper are: atom-ph
31
The categories of this paper are: ao-sci
16
The categories of this paper are: stat
24
The categories of this paper are: dg-ga
33
The categories of this paper are: plasm-ph
8
The categories of this paper are: hep-ex
0
The categories of this paper are: hep-ph
34
The categories of this paper are: chem-ph
14
The categories of this paper are: math-ph
10
The categories of this paper are: q-bio
19
The categories of this paper are: eess
5
The categories of this paper are: gr-qc