The topology-based explanation of the origin of the fractional quantum Hall effect is summarized. The cyclotron braid subgroups crucial for this approach are introduced in order to identify the origin of Laughlin correlations in 2D Hall systems. The so-called composite fermions are explained in terms of the homotopy cyclotron braids. Some new concept for fractional Chern insulator states is formulated in terms of the homotopy condition applied to the Berry field flux quantization.
Jacak, J. , Łydżba, P. and Jacak, L. (2015) Homotopy Approach to Fractional Quantum Hall Effect. Applied Mathematics, 6, 345-358. doi: 10.4236/am.2015.62033.
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