**5. Concluding remarks**

In conclusion, the topological approach to quantum Hall effects is based on a concept of braid groups and their reduction stimulated by an external magnetic field (in 2D spaces). This model can be used to derive hierarchies of FQHE fillings for various two-dimensional structures (including multi-layers), which fit perfectly to the experimental findings. Additionally, it can be used to explain many issues that are believed to be mysterious—the puzzles of quantum Hall structures.
