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

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.

v2: new and improved version implementing comments from referee

References in corpus (4)

• The gauge algebra of double field theory and Courant brackets
• AKSZ-BV Formalism and Courant Algebroid-induced Topological Field Theories
• Letters to Alan Weinstein about Courant algebroids
• Modular Classes of Loday Algebroids

Cited by in corpus (6)

• Split Courant algebroids as $L_{\infty }$-structures
• On the Equivalence of Generalized Ricci Curvatures
• Courant-Dorfman algebras of differential operators and Dorfman connections of Courant algebroids
• Stability of fixed points in Poisson geometry and higher Lie theory
• Higher Multi-Courant Algebroids
• The standard cohomology of regular Courant algebroids