XXXVI Workshop on Geometric Methods in Physics 2-8.07.2017 VI School on Geometry and Physics 26-30.06.2017
 Home First Announcement Second Announcement Travel and local information Participants of Workshop Participants of School Registration Photos Proceedings Previous Workshops Email

# Elizaveta Vishnyakova

## Geometrization of graded manifolds of type $\Delta$

Vector bundles and double vector bundles, or $2$-fold vector bundles, arise naturally for instance as base spaces for algebraic structures such as Lie algebroids, Courant algebroids and double Lie algebroids. It is known that all these structures possess a unified description using the language of supergeometry and graded manifolds of degree $\leq 2$. Indeed, a link has been established between the super and classical pictures by the geometrization process, leading to an equivalence of the category of graded manifolds of degree $\leq 2$ and the category of (double) vector bundles with additional structures.

Our talk is devoted to the geometrization process in the case of $\mathbb Z^r$-graded manifolds of type $\Delta$, where $\Delta$ is a certain weight system and $r$ is the rank of $\Delta$. We establish an equivalence between a subcategory of the category of $n$-fold vector bundles and the category of graded manifolds of type $\Delta$.

 Event sponsored by: University of Bialystok

Webpage by: Tomasz Golinski