Universal Super Vector Bundles
Mohammad Javad Afshari, Saad Varsaie

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.
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Taxonomy
TopicsHomotopy and Cohomology in Algebraic Topology · Advanced Topics in Algebra · Algebraic structures and combinatorial models
