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has been cited by the following article:

• TITLE: Homotopy Approach to Fractional Quantum Hall Effect

  AUTHORS: Janusz Jacak, Patrycja Łydżba, Lucjan Jacak

  KEYWORDS: Quantum Hall Effects, Braid Groups, Homotopy Methods

  JOURNAL NAME: Applied Mathematics, Vol.6 No.2, February 10, 2015

  ABSTRACT: 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.