Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Moduli of spherical tori with one conical point   In this paper we determine the topology of the moduli space
$\mathcal{MS}_{1,1}(\vartheta)$ of surfaces of genus one with a Riemannian
metric of constant curvature $1$ and one conical point of angle
$2\pi\vartheta$. In particular, for $\vartheta\in (2m-1,2m+1)$ non-odd,
$\mathcal{MS}_{1,1}(\vartheta)$ is connected, has orbifold Euler characteristic
$-m^2/12$, and its topology depends on the integer $m>0$ only. For
$\vartheta=2m+1$ odd, $\mathcal{MS}_{1,1}(2m+1)$ has $\lceil{m(m+1)/6}\rceil$
connected components. For $\vartheta=2m$ even, $\mathcal{MS}_{1,1}(2m)$ has a
natural complex structure and it is biholomorphic to $\mathbb{H}^2/G_m$ for a
certain subgroup $G_m$ of $\mathrm{SL}(2,\mathbb{Z})$ of index $m^2$, which is
non-normal for $m>1$.

32
The categories of this paper are: atom-ph
6
The categories of this paper are: astro-ph
15
The categories of this paper are: nucl-ex
37
The categories of this paper are: supr-con
19
The categories of this paper are: eess
25
The categories of this paper are: patt-sol
36
The categories of this paper are: cmp-lg
29
The categories of this paper are: funct-an
34
The categories of this paper are: chem-ph
21
The categories of this paper are: adap-org
13
The categories of this paper are: quant-ph
20
The categories of this paper are: acc-phys
14
The categories of this paper are: math-ph
12
The categories of this paper are: nucl-th
24
The categories of this paper are: dg-ga
1
The categories of this paper are: cs