Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Abelianization of Fuchsian Systems on a 4-punctured sphere and
  applications   In this paper we consider special linear Fuchsian systems of rank $2$ on a
$4-$punctured sphere and the corresponding parabolic structures. Through an
explicit abelianization procedure we obtain a $2-$to$-1$ correspondence between
flat line bundle connections on a torus and these Fuchsian systems. This
naturally equips the moduli space of flat $SL(2,\mathbb C)-$connections on a
$4-$punctured sphere with a new set of Darboux coordinates. Furthermore, we
apply our theory to give a complex analytic proof of Witten's formula for the
symplectic volume of the moduli space of unitary flat connections on the
$4-$punctured sphere.

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The categories of this paper are: gr-qc
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The categories of this paper are: econ
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The categories of this paper are: hep-lat
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The categories of this paper are: adap-org
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The categories of this paper are: quant-ph
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The categories of this paper are: chem-ph
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The categories of this paper are: funct-an
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The categories of this paper are: acc-phys
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The categories of this paper are: nlin
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The categories of this paper are: cmp-lg
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The categories of this paper are: supr-con
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The categories of this paper are: plasm-ph
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The categories of this paper are: atom-ph
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The categories of this paper are: q-bio
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The categories of this paper are: physics
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The categories of this paper are: astro-ph