Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: The quantum Teichmuller space as a noncommutative algebraic object   We consider the quantum Teichmuller space of the punctured surface introduced
by Chekhov-Fock-Kashaev, and formalize it as a noncommutative deformation of
the space of algebraic functions on the Teichmuller space of the surface. In
order to apply it in 3-dimensional topology, we put more attention to the
details involving small surfaces.

9
The categories of this paper are: nlin
17
The categories of this paper are: q-fin
23
The categories of this paper are: solv-int
5
The categories of this paper are: gr-qc
26
The categories of this paper are: bayes-an
37
The categories of this paper are: supr-con
3
The categories of this paper are: physics
6
The categories of this paper are: astro-ph
13
The categories of this paper are: quant-ph
19
The categories of this paper are: eess
20
The categories of this paper are: acc-phys
27
The categories of this paper are: comp-gas
10
The categories of this paper are: q-bio
11
The categories of this paper are: hep-lat
33
The categories of this paper are: plasm-ph
8
The categories of this paper are: hep-ex