Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Gluing Formulas for Volume Forms on Representation Varieties of Surfaces   Let $\Sigma_{g,n}$ be a compact oriented surface with genus $g\geq 2$
bordered by $n$ circles. Due to Witten, the twisted Reidemeister torsion
coincides with a power of the Atiyah-Bott-Goldman-Narasimhan symplectic form on
the space of representations of $\pi_1(\Sigma_{g,0})$ in any semi-simple Lie
group. In the present paper, we first obtain a multiplicative gluing formula
for the twisted Reidemeister torsion of $\Sigma_{g,0}$ in terms of torsions of
$\Sigma_{2,2},$ $\Sigma_{2,1},$ and boundary circles $\mathbb{S}^1.$ Then, by
using Heusener and Porti's results on $\Sigma_{g,n},$ we show that the
symplectic volume form on the representation variety of $\Sigma_{g,0}$ can be
expressed as a product of the holomorphic symplectic volume forms on the
relative representation varieties of surfaces $\Sigma_{2,1}$ and
$\Sigma_{2,2}.$

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The categories of this paper are: physics
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The categories of this paper are: hep-lat
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The categories of this paper are: q-fin
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The categories of this paper are: nucl-th
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The categories of this paper are: bayes-an
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The categories of this paper are: cmp-lg
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The categories of this paper are: hep-ex
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The categories of this paper are: funct-an
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The categories of this paper are: q-bio
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The categories of this paper are: atom-ph
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The categories of this paper are: plasm-ph
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The categories of this paper are: chao-dyn
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The categories of this paper are: comp-gas
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The categories of this paper are: dg-ga
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The categories of this paper are: solv-int
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The categories of this paper are: acc-phys