Euler-Poincare characteristic pair of orientable $\Pi$-symmetric super manifolds

The Euler-Poincare characteristic, or Euler characteristic in short, is a fundamental topological invariant of compact manifolds that plays a crucial role in a variety of geometric and topological situations. From this point of view, we tried to expand this important concept in super geometry. In this article, we introduce Euler-Poincare characteristic pair in the category of $\Pi$-symmetric super manifolds. This is done by finding the self-intersection pair of each super manifold.