Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Characterization of 3-punctured spheres in non-hyperbolic link exteriors   In this paper, we characterize non-hyperbolic 3-component links in the
3-sphere whose exteriors contain essential 3-punctured spheres with
non-integral boundary slopes. We also show the existence of embeddings of some
multibranched surfaces in the 3-sphere which satisfy some homological
conditions to be embedded in the 3-sphere.

1
The categories of this paper are: cs
6
The categories of this paper are: astro-ph
21
The categories of this paper are: adap-org
10
The categories of this paper are: q-bio
37
The categories of this paper are: supr-con
9
The categories of this paper are: nlin
27
The categories of this paper are: comp-gas
5
The categories of this paper are: gr-qc
29
The categories of this paper are: funct-an
30
The categories of this paper are: q-alg
35
The categories of this paper are: mtrl-th
8
The categories of this paper are: hep-ex
22
The categories of this paper are: chao-dyn
32
The categories of this paper are: atom-ph
31
The categories of this paper are: ao-sci
16
The categories of this paper are: stat