Determining the filling factors of fractional quantum Hall states using knot theory

Abstract

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