Courant cohomology, Cartan calculus, connections, curvature, characteristic classes

TL;DR

This paper develops a cohomology theory for Courant algebroids, paralleling classical differential geometry, and introduces characteristic classes using a new connection framework.

Contribution

It provides an explicit description of Courant algebroid cohomology and develops a theory of connections and characteristic classes analogous to classical geometry.

Findings

Explicit cochain complex description for Courant algebroids

Formulation of Courant algebroid connections similar to classical connections

Construction of secondary characteristic classes for Courant algebroids

Abstract

We give an explicit description, in terms of bracket, anchor, and pairing, of the standard cochain complex associated to a Courant algebroid. In this formulation, the differential satisfies a formula that is formally identical to the Cartan formula for the de Rham differential. This perspective allows us to develop the theory of Courant algebroid connections in a way that mirrors the classical theory of connections. Using a special class of connections, we construct secondary characteristic classes associated to any Courant algebroid.