Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Tackling the Trefoils   The classical trefoil is famous for having a three-colouring which
distinguishes it from the unknot. The three-colouring is also notorious for not
distinguishing the right handed from the left handed trefoil. However with a
bit of tweaking the three colours can also be used for this task. What lies
behind the method is a new operation on biracks called doubling which converts
the 3-colour quandle into a biquandle. Colouring with this biquandle
distinguishes the right handed from the left handed trefoil. Equivalently it
defines an element of the homology of the quandle or biquandle classifying
space.

31
The categories of this paper are: ao-sci
29
The categories of this paper are: funct-an
32
The categories of this paper are: atom-ph
15
The categories of this paper are: nucl-ex
17
The categories of this paper are: q-fin
6
The categories of this paper are: astro-ph
13
The categories of this paper are: quant-ph
27
The categories of this paper are: comp-gas
16
The categories of this paper are: stat
11
The categories of this paper are: hep-lat
8
The categories of this paper are: hep-ex
36
The categories of this paper are: cmp-lg
33
The categories of this paper are: plasm-ph
28
The categories of this paper are: alg-geom
21
The categories of this paper are: adap-org
37
The categories of this paper are: supr-con