Communications in Mathematical Physics
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.
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Cueca, Miquel and Mehta, Rajan Amit, "Courant Cohomology, Cartan Calculus, Connections, Curvature, Characteristic Classes" (2021). Mathematics and Statistics: Faculty Publications, Smith College, Northampton, MA.