# A Cartan formula for Courant algebroid cohomology

## Meeting Details

Abstract: It is known that Courant algebroids are in correspondence with degree 2 symplectic dg-manifolds. The standard cochain complex of a Courant algebroid is, by definition, the complex consisting of functions on the corresponding dg-manifold. This implicit definition is difficult to work with directly; for example, in their construction of the modular class, Stienon and Xu defined a weaker naive complex'' as a way of circumventing the standard complex. In my talk, I will explain how, contrary to popular belief, it is possible to give a bracket-and-anchor definition of the standard complex, where the differential is given by a familiar-looking Cartan formula. The tradeoff is that we need to consider cochains that are non-skew-symmetric. As an application, I will explain how the classical theory of connections extends almost verbatim to Courant algebroids. If there is time, I will briefly sketch a construction of higher characteristic classes, generalizing the modular class. This is joint work with Miquel Cueca Ten.