Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Determining the filling factors of fractional quantum Hall states using
  knot theory   In this work a method based on a topological invariance of rational tangles
commonly used in knot theory determines filling factors in the fractional
quantum Hall effect. The main sustain for this hypothesis are the Schubert's
theorems which treats the isotopic between two knots that are numerators of
non-equivalent rational tangles. This isotopic allows to deduce a new formula
for all filling factors. Besides, it opens a new perspective for a future
connection between $N-$particles interaction at different fillings and Berry
phase evaluated along torus knots

37
The categories of this paper are: supr-con
18
The categories of this paper are: econ
2
The categories of this paper are: math
34
The categories of this paper are: chem-ph
5
The categories of this paper are: gr-qc
16
The categories of this paper are: stat
36
The categories of this paper are: cmp-lg
0
The categories of this paper are: hep-ph
10
The categories of this paper are: q-bio
24
The categories of this paper are: dg-ga
21
The categories of this paper are: adap-org
28
The categories of this paper are: alg-geom
17
The categories of this paper are: q-fin
20
The categories of this paper are: acc-phys
12
The categories of this paper are: nucl-th
6
The categories of this paper are: astro-ph