Analytic Approach To a Generalization of Chern Classes in Supergeometry

TL;DR

This paper introduces $ u$ classes, a supergeometric generalization of Chern classes, for super line bundles over $ u$ projective spaces, described via analytic representatives in generalized de Rham cohomology.

Contribution

It presents a novel supergeometric extension of Chern classes and provides their analytic description in the context of supergeometry.

Findings

$ u$ classes generalize Chern classes in supergeometry

Analytic representatives of $ u$ classes are constructed

$ u$ classes are linked to generalized de Rham cohomology

Abstract

Some cohomology elements, called $\nu$ classes, as a supergeneralization of universal Chern classes, are introduced for canonical super line bundles over $\nu$ projective spaces, a novel supergeometric generalization of projective spaces. It is shown that these classes may be described by analytic representatives of elements of generalized de Rham cohomology.