Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Exact G$_2$-structures on compact quotients of Lie groups   We show that the compact quotient $\Gamma\backslash\mathrm{G}$ of a
seven-dimensional simply connected Lie group $\mathrm{G}$ by a co-compact
discrete subgroup $\Gamma\subset\mathrm{G}$ does not admit any exact
$\mathrm{G}_2$-structure which is induced by a left-invariant one on
$\mathrm{G}$.

31
The categories of this paper are: ao-sci
34
The categories of this paper are: chem-ph
20
The categories of this paper are: acc-phys
3
The categories of this paper are: physics
4
The categories of this paper are: cond-mat
27
The categories of this paper are: comp-gas
17
The categories of this paper are: q-fin
19
The categories of this paper are: eess
6
The categories of this paper are: astro-ph
37
The categories of this paper are: supr-con
5
The categories of this paper are: gr-qc
29
The categories of this paper are: funct-an
35
The categories of this paper are: mtrl-th
26
The categories of this paper are: bayes-an
28
The categories of this paper are: alg-geom
9
The categories of this paper are: nlin