
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.
Recommended Citation
Bracken, Paul. 2024. “Recent Topics on Topology - From Classical to Modern Applications.” In Recent Topics on Topology - From Classical to Modern Applications. IntechOpen. https://doi.org/10.5772/intechopen.1003398
Creative Commons 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
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.