  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
