Landau levels in the presence of topological defects

In this paper we study the Landau levels in the presence of topological def ects. We analyse the behaviour of electrons moving in a magnetic field in t he presence of a continuous distribution of disclinations, a magnetic screw dislocation and a dispiration. We focus on the influence of these topologi cal defects on the spectrum of the electron (or hole) in the magnetic field in the framework of the geometric Katanaev-Volovich theory of defects in s olids. The presence of the defect breaks the degeneracy of the Landau level s in different ways depending on the defect. Exact expressions for energies and eigenfunctions are found for all cases. Using Kaluza-Klein theory we s olve the Landau level problem for a dispiration and compare the results wit h the ones obtained in the previous cases.