School of Mathematical and Statistical Sciences Faculty Publications and Presentations

Document Type

Book Chapter

Publication Date

11-2024

Abstract

The quantum Hall effects are an excellent example of physical systems where topology plays a major role in accounting for the physical observations. It is shown that the conductivity that appears in the quantum Hall effect is a topological invariant. It is illustrated how a fiber bundle over a torus can be constructed producing a geometry in which the system can be referred. The fractional effect can be studied by introducing homotopy and associated braid groups. Filling fractions can be obtained as a consequence of commensurability relations.

Comments

© The Author(s). Licensee IntechOpen. This chapter is distributed under the terms of the Creative Commons 4.0 International License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Creative Commons License

Creative Commons Attribution 4.0 International License
This work is licensed under a Creative Commons Attribution 4.0 International License.

Publication Title

Recent Topics on Topology - From Classical to Modern Applications

DOI

http://doi.org/10.5772/intechopen.1007560

Included in

Mathematics Commons

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