Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Quantization of Teichm\"uller spaces and the quantum dilogarithm   The Teichm\"uller space of punctured surfaces with the Weil-Petersson
symplectic structure and the action of the mapping class group is realized as
the Hamiltonian reduction of a finite dimensional symplectic space where the
mapping class group acts by symplectic rational transformations. Upon
quantization the corresponding (projective) representation of the mapping class
group is generated by the quantum dilogarithms.

27
The categories of this paper are: comp-gas
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The categories of this paper are: bayes-an
5
The categories of this paper are: gr-qc
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The categories of this paper are: math-ph
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The categories of this paper are: stat
23
The categories of this paper are: solv-int
17
The categories of this paper are: q-fin
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The categories of this paper are: alg-geom
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The categories of this paper are: funct-an
4
The categories of this paper are: cond-mat
1
The categories of this paper are: cs
36
The categories of this paper are: cmp-lg
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The categories of this paper are: supr-con
24
The categories of this paper are: dg-ga
9
The categories of this paper are: nlin
21
The categories of this paper are: adap-org