Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Fundamental domains in ${\rm PSL}(2,{\mathbb R})$ for Fuchsian groups   In this paper, we provide a necessary and sufficient condition for a set in
${\rm PSL}(2,{\mathbb R})$ or in $T^1{\mathbb H}^2$ to be a fundamental domain
for a given Fuchsian group via its respective fundamental domain in the
hyperbolic plane ${\mathbb H}^2$.

15
The categories of this paper are: nucl-ex
0
The categories of this paper are: hep-ph
27
The categories of this paper are: comp-gas
32
The categories of this paper are: atom-ph
26
The categories of this paper are: bayes-an
8
The categories of this paper are: hep-ex
5
The categories of this paper are: gr-qc
9
The categories of this paper are: nlin
6
The categories of this paper are: astro-ph
17
The categories of this paper are: q-fin
23
The categories of this paper are: solv-int
7
The categories of this paper are: hep-th
14
The categories of this paper are: math-ph
3
The categories of this paper are: physics
21
The categories of this paper are: adap-org
25
The categories of this paper are: patt-sol