arXiv subjects

Mehdi Ghorbani

Publications and source records attributed to Mehdi Ghorbani.

2 recordsLinked to original sources

arXiv2025

Euler-Poincare characteristic pair of orientable supermanifolds

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 $Π$-symmetric supermanifolds.

math.DG↗

arXiv2025

Supertransversality and $Π$-symmetric supermanifolds

The main objective of this article is to extend the concept of transversality to supergeometry. Transversality has two important properties in the classical case, namely " stability" and " genericity", which we show in the following that in the category of smooth supermanifolds, supertransversality has stable property. By extending Sard's theorem to supergeometry, genericity property is proved. In the final section, we examine transversality in the category of $Π$-symmetric supermanifolds. The theory presented here is a step towards an extension of the concept of Euler-Poincaré characteristic to supermanifolds.

math.DG↗