Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: On a move reducing the genus of a knot diagram   For a knot diagram we introduce an operation which does not increase the
genus of the diagram and does not change its representing knot type. We also
describe a condition for this operation to certainly decrease the genus. The
proof involves the study of a relation between the genus of a virtual knot
diagram and the genus of a knotoid diagram, the former of which has been
introduced by Stoimenow, Tchernov and Vdovina, and the latter by Turaev
recently. Our operation has a simple interpretation in terms of Gauss codes and
hence can easily be computer-implemented.

19
The categories of this paper are: eess
30
The categories of this paper are: q-alg
8
The categories of this paper are: hep-ex
27
The categories of this paper are: comp-gas
16
The categories of this paper are: stat
34
The categories of this paper are: chem-ph
1
The categories of this paper are: cs
0
The categories of this paper are: hep-ph
14
The categories of this paper are: math-ph
29
The categories of this paper are: funct-an
11
The categories of this paper are: hep-lat
3
The categories of this paper are: physics
32
The categories of this paper are: atom-ph
28
The categories of this paper are: alg-geom
20
The categories of this paper are: acc-phys
17
The categories of this paper are: q-fin