opposite sides of the circumference of the nanotube that carry current along the length of the nanotube but in opposite directions. The quantization is approximate. This is to be contrasted with the following properties of Hall effect discussed in the present work. It appears when the Fermi energy is in the gap between the conduction and valence bands. All the current travels in one direction throughout the whole sample. The Hall quantization of the Hall conductivity is sharp.

The conclusion is that the Hall effect discussed in this paper has not yet been found in the context of carbon nanotubes. But is it there? The topological theory cannot answer this question. It only works for systems that are much larger than the periodicity of the magnetic field, whereas the length of the nanotube system in the circumferential direction is the same as the periodicity of the magnetic field. It is not clear if the intuitive argument presented in this section can be applied either. It also involves viewing the system with a spatial resolution that is larger than the periodicity of the magnetic field. The question therefore remains open.

Examples {#six}
========

[*Example 1:*]{} As a simple example that illustrates 