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Courant Cohomology, Cartan Calculus, Connections, Curvature, Characteristic Classes

2020; Springer Science+Business Media; Volume: 381; Issue: 3 Linguagem: Inglês

10.1007/s00220-020-03894-y

1432-0916

Miquel Cueca, Rajan Amit Mehta,

Nonlinear Waves and Solitons

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.