  Topological characteristics reveal important physical properties of plasma
structures and astrophysical processes. Physical parameters and constraints are
linked with topological invariants, which are important for describing magnetic
reconnection scenarios. We analyze stationary non-ideal Ohm's law concerning
the Poincare classes of all involved physical fields in 2D by calculating the
corresponding topological invariants of their Jacobian (here: particularly the
eigenvalues) or Hessian matrices. The magnetic field is assumed to have a cusp
structure, and the stagnation point of the plasma flow coincides with the cusp.
We find that the stagnation point must be hyperbolic. Furthermore, the
functions describing both the resistivity and the Ohmic heating have a saddle
point structure, being displaced with respect to the cusp point. These results
imply that there is no monotonous relation between current density and
anomalous resistivity in the case of a 2D standard magnetic cusp.
