Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: On the welded Tube map   This note investigates the so-called Tube map which connects welded knots,
that is a quotient of the virtual knot theory, to ribbon torus-knots, that is a
restricted notion of fillable knotted tori in the 4-sphere. It emphasizes the
fact that ribbon torus-knots with a given filling are in one-to-one
correspondence with welded knots before quotient under classical Reidemeister
moves and reformulates these moves and the known sources of non-injectivity of
the Tube map in terms of filling changes.

9
The categories of this paper are: nlin
28
The categories of this paper are: alg-geom
26
The categories of this paper are: bayes-an
21
The categories of this paper are: adap-org
23
The categories of this paper are: solv-int
15
The categories of this paper are: nucl-ex
33
The categories of this paper are: plasm-ph
34
The categories of this paper are: chem-ph
20
The categories of this paper are: acc-phys
24
The categories of this paper are: dg-ga
37
The categories of this paper are: supr-con
10
The categories of this paper are: q-bio
32
The categories of this paper are: atom-ph
35
The categories of this paper are: mtrl-th
5
The categories of this paper are: gr-qc
12
The categories of this paper are: nucl-th