Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Braids in trivial braid diagrams   We show that every trivial 3-strand braid diagram contains a disk, defined as
a ribbon ending in opposed crossings. Under a convenient algebraic form, the
result extends to every Artin--Tits group of dihedral type, but it fails to
extend to braids with 4 strands and more. The proof uses a partition of the
Cayley graph and a continuity argument.

9
The categories of this paper are: nlin
0
The categories of this paper are: hep-ph
12
The categories of this paper are: nucl-th
20
The categories of this paper are: acc-phys
1
The categories of this paper are: cs
6
The categories of this paper are: astro-ph
25
The categories of this paper are: patt-sol
5
The categories of this paper are: gr-qc
10
The categories of this paper are: q-bio
15
The categories of this paper are: nucl-ex
31
The categories of this paper are: ao-sci
27
The categories of this paper are: comp-gas
17
The categories of this paper are: q-fin
29
The categories of this paper are: funct-an
19
The categories of this paper are: eess
21
The categories of this paper are: adap-org