Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Unions of 3-punctured spheres in hyperbolic 3-manifolds   We classify the topological types for the unions of the totally geodesic
3-punctured spheres in orientable hyperbolic 3-manifolds. General types of the
unions appear in various hyperbolic 3-manifolds. Each of the special types of
the unions appears only in a single hyperbolic 3-manifold or Dehn fillings of a
single hyperbolic 3-manifold. Furthermore, we investigate bounds of the moduli
of adjacent cusps for the union of linearly placed 3-punctured spheres.

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The categories of this paper are: adap-org
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The categories of this paper are: supr-con
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The categories of this paper are: atom-ph
7
The categories of this paper are: hep-th
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The categories of this paper are: dg-ga
1
The categories of this paper are: cs
35
The categories of this paper are: mtrl-th
3
The categories of this paper are: physics
9
The categories of this paper are: nlin
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The categories of this paper are: chao-dyn
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The categories of this paper are: math-ph
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The categories of this paper are: hep-lat
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The categories of this paper are: cmp-lg
8
The categories of this paper are: hep-ex
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The categories of this paper are: econ
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The categories of this paper are: nucl-ex