  This work discusses the effect of topology in the frame of direct Coulomb
interactions, considering two distinct geometries, namely the Hall bar and the
Corbino disc. In the mainstream approaches to the quantized Hall effect, the
consequences of interactions are usually underestimated. Here, we investigate
the electron number density, potential and current distributions within the
screening theory that considers electron-electron interactions. Inclusion of
direct Coulomb interaction and realistic boundary conditions result in local
metal-like compressible and (Topological) insulator-like incompressible
regions. Consequently, we show that the bulk of both geometries in coordinate
space is not incompressible throughout the quantized Hall plateau. Furthermore,
placing two inner contacts within the Hall bar geometry shows that the
quantization is unaffected by changing the genus number in real space. Finally,
we propose novel experiments which will enable us to distinguish the
topological properties of the two geometries in the configuration space.
