For any regular Courant algebroid, we construct a characteristic class à la Chern-Weil. This intrinsic invariant of the Courant algebroid is a degree-3 class in its naive cohomology. When the Courant algebroid is exact, it reduces to the Ševera class in H3DR(M). On the other hand, when the Courant algebroid is a quadratic Lie algebra g, it coincides with the class of the Cartan 3-form in H3(g). We also give a complete classification of regular Courant algebroids and discuss its relation to the characteristic class.
All Science Journal Classification (ASJC) codes
- Geometry and Topology