Universal Super Vector Bundles

TL;DR

This paper introduces { u}-grassmannians and a universal super vector bundle, extending homotopy classification theorems in supergeometry, providing a foundational framework for super vector bundle theory.

Contribution

It presents a new class of Grassmannians and a universal super vector bundle, extending classical homotopy classification results to supergeometry.

Findings

Defined { u}-grassmannians as a generalization of Grassmannians

Constructed a canonical super vector bundle over { u}-grassmannians

Extended homotopy classification theorems to supergeometry

Abstract

A new generalization of Grassmannians, called {\nu}-grassmannians, and a canonical super vector bundle over this new space, say {\Gamma}, are introduced. Then, constructing a Gauss supermap of a super vector bundle, the universal property of {\Gamma} is discussed. Finally, we generalize one of the main theorems of homotopy classification for vector bundles in supergeometry.