Euler-Poincare characteristic pair of orientable supermanifolds

Abstract

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 on this important concept in supergeometry. In this article, we introduce the Euler-Poincare characteristic pair in the supergeometry. In the final section, we examine transversality in the category of $\Pi$-symmetric supermanifolds.