Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Toroidal embeddings of abstractly planar graphs are knotted or linked   We give explicit deformations of embeddings of abstractly planar graphs that
lie on the standard torus $T^2 \subset \mathbb{R}^3$ and that contain neither a
nontrivial knot nor a nonsplit link into the plane. It follows that ravels do
not embed on the torus. Our results provide general insight into properties of
molecules that are synthesized on a torus.

17
The categories of this paper are: q-fin
25
The categories of this paper are: patt-sol
5
The categories of this paper are: gr-qc
12
The categories of this paper are: nucl-th
21
The categories of this paper are: adap-org
6
The categories of this paper are: astro-ph
33
The categories of this paper are: plasm-ph
19
The categories of this paper are: eess
15
The categories of this paper are: nucl-ex
31
The categories of this paper are: ao-sci
0
The categories of this paper are: hep-ph
24
The categories of this paper are: dg-ga
8
The categories of this paper are: hep-ex
37
The categories of this paper are: supr-con
16
The categories of this paper are: stat
22
The categories of this paper are: chao-dyn