On higher-dimensional Courant algebroids

TL;DR

This paper introduces a transgression functor that connects higher-dimensional Courant algebroids on manifolds to Lie algebroids on their shifted tangent bundles, advancing the understanding of their geometric structures.

Contribution

It defines a new transgression functor linking higher-dimensional Courant algebroids to Lie algebroids on shifted tangent bundles, providing a novel perspective in differential geometry.

Findings

Establishment of the transgression functor for higher-dimensional Courant algebroids

Connection between Courant algebroids and Lie algebroids on shifted tangent bundles

New framework for studying geometric structures in higher dimensions

Abstract

We define the transgression functor which associates to a (higher-dimensional) Courant algebroid on a manifold a Lie algebroid on the shifted tangent bundle of the manifold.