Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Some properties of simple minimal knots   A minimal knot is the intersection of a topologically embedded branched
minimal disk in $\mathbb{R}^4$ $\mathbb{C}^2 $ with a small sphere centered at
the branch point. When the lowest order terms in each coordinate component of
the embedding of the disk in $\mathbb{C}^2$ are enough to determine the knot
type, we talk of a simple minimal knot. Such a knot is given by three integers
$N < p,q$; denoted by $K(N,p,q)$, it can be parametrized in the cylinder as
$e^{i\theta}\mapsto (e^{Ni\theta},\sin q\theta,\cos p\theta)$. From this
expression stems a natural representation of $K(N,p,q)$ as an $N$-braid. In
this paper, we give a formula for its writhe number, i.e. the signed number of
crossing points of this braid and derive topological consequences. We also show
that if $q$ and $p$ are not mutually prime, $K(N,p,q)$ is periodic. Simple
minimal knots are a generalization of torus knots.

10
The categories of this paper are: q-bio
36
The categories of this paper are: cmp-lg
3
The categories of this paper are: physics
17
The categories of this paper are: q-fin
4
The categories of this paper are: cond-mat
9
The categories of this paper are: nlin
30
The categories of this paper are: q-alg
13
The categories of this paper are: quant-ph
20
The categories of this paper are: acc-phys
28
The categories of this paper are: alg-geom
35
The categories of this paper are: mtrl-th
8
The categories of this paper are: hep-ex
16
The categories of this paper are: stat
26
The categories of this paper are: bayes-an
14
The categories of this paper are: math-ph
0
The categories of this paper are: hep-ph