Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Geometrization of almost extremal representations in $\text{PSL}_2\Bbb
  R$   Let $S$ be a closed surface of genus $g$. In this paper, we investigate the
relationship between hyperbolic cone-structure on $S$ and representations of
the fundamental group into $\text{PSL}_2\Bbb R$. We consider surfaces of genus
greater than $g$ and we show that, under suitable conditions, every
representation $\rho:\pi_1 S\longrightarrow \text{PSL}_2\Bbb R$ with Euler
number $\mathcal{E}(\rho)=\pm\big(\chi(S)+1\big)$ arises as holonomy of a
hyperbolic cone-structure $\sigma$ on $S$ with a single cone point of angle
$4\pi$. From this result, we derive that for surfaces of genus $2$ every
representation with $\mathcal{E}(\rho)=\pm1$ arises as the holonomy of some
hyperbolic cone-structure.

5
The categories of this paper are: gr-qc
26
The categories of this paper are: bayes-an
18
The categories of this paper are: econ
22
The categories of this paper are: chao-dyn
16
The categories of this paper are: stat
28
The categories of this paper are: alg-geom
25
The categories of this paper are: patt-sol
0
The categories of this paper are: hep-ph
10
The categories of this paper are: q-bio
20
The categories of this paper are: acc-phys
27
The categories of this paper are: comp-gas
1
The categories of this paper are: cs
17
The categories of this paper are: q-fin
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The categories of this paper are: astro-ph
15
The categories of this paper are: nucl-ex
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The categories of this paper are: eess