Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Infra-solvmanifolds of $\Sol_1^4$-geometry   The purpose of this paper is to classify all compact manifolds modeled on the
4-dimensional solvable Lie group $Sol_1^4$. The maximal compact subgroup of
$Isom(Sol_1^4)$ is $D_4=\mathbb Z_4\rtimes\mathbb Z_2$. We shall exhibit an
infra-solvmanifold with $Sol_1^4$-geometry whose holonomy is $D_4$. This
implies that all possible holonomy groups do occur; $\{1\}$, $\mathbb Z_2$ (5
families), $\mathbb Z_4$, $\mathbb Z_2\times\mathbb Z_2$ (5 families),and
$\mathbb Z_4\rtimes\mathbb Z_2$ (2 families). This includes the classification
of 3-dimensional infra-$Sol$ manifolds.

32
The categories of this paper are: atom-ph
30
The categories of this paper are: q-alg
1
The categories of this paper are: cs
7
The categories of this paper are: hep-th
12
The categories of this paper are: nucl-th
24
The categories of this paper are: dg-ga
33
The categories of this paper are: plasm-ph
11
The categories of this paper are: hep-lat
37
The categories of this paper are: supr-con
26
The categories of this paper are: bayes-an
22
The categories of this paper are: chao-dyn
5
The categories of this paper are: gr-qc
27
The categories of this paper are: comp-gas
34
The categories of this paper are: chem-ph
17
The categories of this paper are: q-fin
29
The categories of this paper are: funct-an