Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Discrete representations of finitely generated groups into ${\rm
  PSL}(2,\mathbb{R})$   We prove a factorization theorem for Fuchsian groups similar to those proved
by Agol and Liu for 3-manifold groups. As an application, we build
Makanin-Razborov diagrams, which parametrize the collection of all discrete
representations from an arbitrary but fixed finitely generated group $G$ to
${\rm PSL}(2, \mathbb{R})$. We define a new class of groups called ${\rm
PSL}(2, \mathbb{R})$-discrete limit groups and then use the factorization
theorem to obtain useful information about this class of groups.

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The categories of this paper are: bayes-an
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The categories of this paper are: quant-ph
6
The categories of this paper are: astro-ph
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The categories of this paper are: q-fin
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The categories of this paper are: alg-geom
22
The categories of this paper are: chao-dyn
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The categories of this paper are: cmp-lg
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The categories of this paper are: mtrl-th
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The categories of this paper are: funct-an
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The categories of this paper are: eess
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The categories of this paper are: stat
1
The categories of this paper are: cs
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The categories of this paper are: comp-gas
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The categories of this paper are: nucl-th
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The categories of this paper are: patt-sol
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The categories of this paper are: solv-int